We're engineers (or academics), pedantry is occasionally a hill we die on.
Trying to be precise in language allows you to communicate an idea the most effective way, imo, and at the end of the day that's you're goal. At least it should be in technical writing. If the reader has to pause when they see "codes" instead of "code" because it's just a bit off then that is a tiny failing in your communication.
Definitely not the end of the world, definitely not something to be an asshole about, but it is something I would maybe politely correct if I knew the person well enough.
Also don't take this for me saying I'm perfect in my written communication. I still don't know how to use commas and I've had them explained to me from all grammatical standpoints multiple times. Trying is all you can do.
Comp sci vs the natural sciences have an interesting split on this (though blurring more recently). Computer science tends to use "code" as a collective noun. Traditional usage in the natural sciences and parts of engineering is that "a code" (singular) is a single routine or piece of software to carry out some kind of numerical calculation or simulation. Then "codes" is just the normal plural when talking about more than one of them. So you find papers talking about things like "a new code for simulating preheating" [1] or "benchmarking simulation codes" [2].
That's very interesting, I've limited exposure to programming in the natural sciences so I've only really experienced the collective noun usage.
I had thought "a code" and then "codes" may have come down from the punch card era of programming where as you said it would be more of single routine for a specific computation which I guess then would have filtered down into scientific computing as programming evolved through fortran and others and now it seems it's all merging back together.