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What you are looking for is isomorphic to the group ((Z / 2Z)^n, +) that you can build in Sage in many ways. For example

sage: Zmod(2) ^ 5
Vector space of dimension 5 over Ring of integers modulo 2

Concerning the module question, I don't see any link with the first part. You seem to want to use (Zmod(2), +, x) (this time as a ring).