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We consider q-matroids and their associated classical matroids derived from Gabidulin rank-metric codes. We express the generalized rank weights of a Gabidulin rank-metric code in terms of Betti numbers of the dual classical matroid associated to the q-matroid corresponding to the code. In our main result, we show how these Betti numbers and their elongations determine the generalized weight polynomials for q-matorids, in particular, for the Gabidulin rank-metric codes. In addition, wearXiv:2106.10993v3 fatcat:rvl6djeniranjeldmrlo7wriry