  An important strength of the $q$-ary stabilizer quantum codes is that they
can be constructed from Hermitian self-orthogonal $q^2$-ary linear codes. We
prove that this result can be extended to $q^{2^\ell}$-ary linear codes, $\ell
> 1$, and give a result for easily obtaining codes of the last type. As a
consequence we provide several new binary stabilizer quantum codes which are
records according to \cite{codet} and new $2 \neq q$-ary ones improving others
in the literature.
