A symplectic space with $p$-groups of operators over a field of characteristic $p$

Let $K$ be a field of nonzero characteristic pne2, let $G$ be a finite $p$-group, and let $M$ be a nondegenerate finite-dimensional symplectic space over $K$ with the matching structure of a $G$-module. It is proven that if $M$ is a free $K[G]$-module then there exists in $M$ a normal basis with a canonical Gram matrix.