Though it is ultimately up to the DM, I would say that in the context of the invocation, you would be able to read codes, including thieves cant. The invocation says (PHB 111, emphasis mine):
You can read all writing.
I think some people don't understand that to read something, means that you understand its meaning. Oxford dictionary defines read as (emphasis mine):
look at and comprehend the meaning of (written or printed matter) by
mentally interpreting the characters or symbols of which it is
composed.
Thus, when you can read something, you can understand it. Furthermore, the invocation states (emphasis mine):
You can read all writing.
Let me provide you with the Oxford definition of all (emphasis mine):
used to refer to the whole quantity or extent of a particular group
or thing.
In this case, the "particular group of thing" is writing. Ergo, "all writing" means the whole extent of written things. So, anything that is written is included in this. If a specific code, thieves cant, or any other jargon is in written form, it is included in "all writing." Thus, anyone who has the eyes of the rune keeper invocation can understand its meaning.