My question is below:
Prove that if a binary $(n,M,d)$-code exists for which $d$ is even, then a binary $(n,M,d)$-code exists for which each codeword has even weight.
(Hint: Do some puncturing and extending.)
Breaking this down to individual steps. Assume that $d=2t$ is an even integer. Assume that an $(n,M,d)$ code $C$ exists.
Observe that we did not assume linearity at any step.