Hyperplanes of DW(2n-1,q)DW(2n-1,q), q≠2q≠2, without ovoidal quads

We determine all hyperplanes of DW(2n-1,q)DW(2n-1,q), q≠2q≠2, without ovoidal quads. We will show that each such hyperplane either consists of all maximal singular subspaces of W(2n-1,q)W(2n-1,q) which meet a given (n-1)(n-1)-dimensional subspace of PG(2n-1,q)PG(2n-1,q) or (only when q   is even) arises from the spin-embedding of DW(2n-1,q)DW(2n-1,q).