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Reading the Latin version of Wikipedia, I noticed that the term "programming language" was translated in many ways.
Depending on the page, you can find almost any combination of lingua/codex/cifra and programmandi/programmationis/computatralis/programmatica.
Is there a version that is better Latin than the others?
Better is subjective, and therefore technically not answerable on StackExchange. Since this is essentially a modern invention, it's impossible to know how the ancient Romans or even the various speakers in the Middle Ages would have constructed the terminology.
However, my vote goes to for "programming language" goes to:
lingua programmatica.
There's a good analogue for programmatica with the ancient grammatica, "belonging to grammar." Given programma = "program" (from this link), programmaticus, -a, -um is a fine derivation.
Of course, it isn't perfect per se, since if someone saw this in antiquity, they would think it's the language of proclamations, but a long history has changed the word "program" in English, and English bequeathed it to the rest of the world with this new sense. So there's no shame in Latin adopting it, too.
As far as the other options you list:
cifra is not ancient Latin and is such a weird choice. It comes from the Arabic sifr meaning "zero." Not only that, it probably doesn't antedate the original Romance borrowings (not sure of exact dates, but my guess would be Spanish got it first). It could mean zero, numeral, or cypher, but it's a big stretch to get to "language" from that.
codex, per the above link, is more properly the "code." It should refer more to the written product rather than the production.
programmandi could work, but it translates more closely to "the language of programming." It makes it seem as if there is only one.
programmationis would refer to the language of a particular program instead of describing what sort of language it is.
computatralis would refer to the language of the computer. It could refer to binary or maybe assembly, but I have a hard time seeing this as a general term for all programming languages. But it's possible!
