  Many $q$-ary stabilizer quantum codes can be constructed from Hermitian
self-orthogonal $q^2$-ary linear codes. This result can be generalized to $q^{2
m}$-ary linear codes, $m > 1$. We give a result for easily obtaining quantum
codes from that generalization. As a consequence we provide several new binary
stabilizer quantum codes which are records according to \cite{codet} and new
$q$-ary ones, with $q \neq 2$, improving others in the literature.
