The problem is stated as follows:
Let C be a binary linear code of length n, dimension k and distance d and assume that C contains at least one element of odd weight.
Let C' be the subset of C consisting of all code words of even weight. Show that C' is a linear code of length n, dimension k −1 and distance d' where d' > d if d is odd and d'= d if d is even
How would you approach this problem?
Prof. Lahtonen's comment settles it (as usual!), but I will try to elaborate a bit. If the code $\mathcal{C}$ has at least $1$ odd weight codeword, it is an independent vector as no $\mathbb{F}_2$-linear combination of the remaining even codewords can generate it. Hence the dimension of $\mathcal{C'}$ is $k -1$.
The distance is easy: if $d$ is odd, that's the weight of an odd codeword, and so $d'> d$; the other case follows.