Comment by kjs3
I don't know anyone who doesn't say "I wrote X assembler" with complete understanding by all involved, and I definitely don't know anyone so pedantic they said "acksually, it's 'I wrote X assembly code'". I guess none of the dozens of assembly code makers or whatever I've know over the last 40 years was enough of a stickler. Or care one way or another.
I also understood the title to mean writing an assembler rather than writing assembly language code, and I've never heard anyone refer to writing assembly as writing assembler (or heard anyone who writes assembly referred to as an "assembly code maker", nor anyone who writes in any language referred to as an "<language> code maker").
I could imagine such phrasing being done by non-native English speakers, of which I'm have no doubt that there are a significant number.
My (unresearched) guess is that this is simply different dialects of speakers emerging with respect to informal references over the decades.