We prove that the natural isomorphism$\mathbb {F}_{2^{h}}\cong \mathbb {F} _{2}^{h}$induces a bijection between stabilizer codes on n quqits with local dimension$q=2^{h}$and binary stabilizer codes on hn qubits. This allows us to describe these codes geometrically: a stabilizer code over a field of even order corresponds to a so-called quantum set of symplectic polar spaces. Moreover, equivalent stabilizer codes have a similar geometry, which can be used to prove the uniqueness of a$[\![{4,0,3}]\!]_{4}$stabilizer code and the nonexistence of both a$[\![{7,1,4}]\!]_{4}$and an$[\![{8,0,5}]\!]_{4}$stabilizer code.

We determine the diameter of generalized Grassmann graphs and the zero forcing number of some generalized Johnson graphs, generalized Grassmann graphs and the Hamming graphs. Our work extends several previously known results.