Uniqueness of code-loop representations by degree and type

Let $L$ be a code loop, and let $V_{1}$ and $V_{2}$ be representations of $L$. The degree-and-type uniqueness conjecture. If $V_{1}$ and $V_{2}$ have the same degree and type, then they are isomorphic. The claim is motivated by the fact that, for code loops of ranks 3 and 4, the type determines the loop up to isomorphism; whether the analogous uniqueness holds in general is left open.