  The weight distribution of an error correcting code is a crucial statistic in
determining it's performance. One key tool for relating the weight of a code to
that of it's dual is the MacWilliams Identity, first developed for the Hamming
metric. This identity has two forms: one is a functional transformation of the
weight enumerators, while the other is a direct relation of the weight
distributions via (generalised) Krawtchouk polynomials. The functional
transformation form can in particular be used to derive important moment
identities for the weight distribution of codes. In this paper, we focus on
codes in the skew rank metric. In these codes, the codewords are skew-symmetric
matrices, and the distance between two matrices is the skew rank metric, which
is half the rank of their difference. This paper develops a $q$-analog
MacWilliams Identity in the form of a functional transformation for codes based
on skew-symmetric matrices under their associated skew rank metric. The method
introduces a skew-$q$ algebra and uses generalised Krawtchouk polynomials.
Based on this new MacWilliams Identity, we then derive several moments of the
skew rank distribution for these codes.
