I am a coder who codes programmes.
Or, a programmer who programmes programmes.
Or, a coder who programmes code.
Etc. Etc.
English is an odd language with many rules, to which there are more exceptions than cases that obey the rules. Relying on English grammar to prove a point is a fool's errand.
The retired Vicar (Pastor) in my village holds a doctorate in English, he is a very entertaining gentleman who has described English as "Three languages, standing on each others shoulders dressed in a long coat trying to buy a pint."
His other genius observation was "English is the sort of language that hangs around in dark alleys and mugs other language for their vocabulary!"