The generalized Hamming polynomial reconstruction formula for combinatroids

Let $M=(E,\rho)$ be a combinatroid, set $n=|E|$ and $k=\rho(E)$, and let $W^{(r)}(x,y,q)$ denote its $r$-generalized Hamming weight enumerator, defined for $1\leq r\leq n$ by

$$W^{(r)}(x,y,q):=\frac{1}{\langle r\rangle_q}\sum_{j=0}^r \left[\begin{array}{c}r\\ j\end{array}\right]_q(-1)^{r-j}q^{\binom{r-j}{2}}(x-y)^{n-k}y^kT_M\left(\frac{x}{y},\frac{x+(q^j-1)y}{x-y}\right).$$

Generalized Hamming polynomial reconstruction conjecture. The Tutte polynomial satisfies

$$T_M(x,y)=x^n(x-1)^{k-n}\sum_{r=0}^{n-k}\left(\prod_{j=0}^{r-1}\bigl((x-1)(y-1)-q^j\bigr)\right)W^{(r)}(1,1/x,q).$$

This formula proposes that the Tutte polynomial of a combinatroid can be reconstructed from its generalized Hamming weight enumerators. The supplied text does not indicate whether the statement has been proved or disproved.