Yeah, I think their code should somewhat reflect their view that each individual has their own free-will and thus is able to define their own fate individually, kind of like existentialism.
I think, because of this, they should not have a hierarchy with designated leader(s) or any type of elitist council, but should instead reflect the principles of a more heteroarchical form of community.
However, they also acknowledge and accept the intangible/undefinable ways in which everything in the universe is interconnected and dependant upon each other, therefore also beseeching responsibility and forethought for each person's course of action within it, and the comprehension of each act's context.
Based upon these premises, they could also implore that there is no such thing as a - sorry, but forgive the pun - 'universal' truth, as everything is relative and consequently every experience is subjective too.
This is because the universe is in a constant flux, and nothing can be pinned down, or perfectly defined.
Thus the universe seems as though it is in chaos, but it is instead that through this one truth ("prepare for a paradox, time"), the only way to find reassurance in this realm is to accept that there is no assurance in anything.
This "one truth" that 'controls', or rather, watches over (omnisciently) everything, is in fact, the force, as it is what binds one and all together. Thus higher meaning has to be found through becoming attuned to, and becoming one with the force.
Here is a really, rather rough draft of how these elements could be included within their code:
In chaos there is balance
In balance there is the order of all things
In the order of things one can free themself
In freedom there is choice
In choice there is responsibility
In responsibility there is the force
Kind of ambivalent (but hey, they're grey - that's the point) but also clear and simple as to how they view existence, but also being open-ended in how these teachings can be taken through into the corporeal world in a practical fashion.
It is not the preaching of a set of moral values, but rather a philosphy, a way of thinking about the universe and life (and generally existence) within it.
The Jedi and the Sith both claim to fully understand the universe, the force's, and our roles within it (or at the very least its core/foundations) - they think they have discovered the beginnings of "the truth".
The grey would not be so self-righteous nor arrogant, only asking of the students of whom they train that they recognise, in fact, that such a thing is undiscovered (if locatable at all), and do not tell their students how to interact with the universe, but how to look internally within themselves first and foremost and make their own judgements (always questioning everything around them) as what to do (but always keep in mind that such judgements are only applicable to themself alone, and take no further meaning other than what they take from it).
And also unlike the Jedi or Sith, they do not train their students to go out into the world to literally enforce a type of ideology upon it, but let the individual make their own way in life, as they see fit, and only ask of them that they consider all perspectives, never blinding or limiting themselves to any one extreme viewpoint, as this is only seeking to achieve meaning in the universe through oversimplification and a denial of its core nature.
Now, this referance to "responsibility" is not designed to be taken in the same vein as how a Jedi might mean the word - it does not denote a sentiment of morality or conscience, but rather an acceptance as to one's own influence and role within the galaxy, no matter what the consequencies may be of any given act, light or dark, a mixture, inbetween or neither.
Like Kreia though, they do not believe that this is an excuse to do nothing (or as little as physically possible), believing in a similar principle to that of "apathy is death".
As a side note (and a superficial detail), could they not have their own spectrum (possibly unofficially though) of designated lightsaber colours? Perhaps they could use such unassigned colours as orange, bronze, silver, white, cyan, viridian, (maybe even yellow, as it is not recognised within the films) etc. That would be awesome