product code = 'kod (JAKI?) produkcyjny'
product's code = 'kod (KOGO/CZEGO?) produktu'
And some other examples:
the cat eyes = '(JAKIE?) kocie oczy'
the cat's eyes = 'oczy (KOGO?CZEGO?) kota'
the car tyres = 'opony (JAKIE?) samochodowe'
the car's tyres = 'opony (KOGO?CZEGO?) samochodu'
You must remember that at school students are normally taught not to use (' + s) with nouns which don't refer to people and animals. So:
'the car's tyres' should be 'the tyres of the car'.