I've been thinking about equivalence of codes (two codes that are equal up to order of positions of the letters, or permutations of the letters in a fixed position).

It is obvious that if we have two codes with the same distance $d$, it doesn't mean they are equivalence; nor if they have the same set of distances.

However, I thought about listing the distances and counting them, that is, make a list of the type "there are $n_1$ pairs of words in the code with distance $1$, $n_2$ pairs of words that differ only in two positions, $n_3 \ldots$"

It is not difficult to see that this criterion does not imply equivalence if we talk about ternary codes; but what if we take binary codes? I have a gut feeling it's wrong too, but can't think of a counter example.