  In 2011, Guruswami-H{\aa}stad-Kopparty \cite{Gru} showed that the
list-decodability of random linear codes is as good as that of general random
codes. In the present paper, we further strengthen the result by showing that
the list-decodability of random {\it Euclidean self-orthogonal} codes is as
good as that of general random codes as well, i.e., achieves the classical
Gilbert-Varshamov bound. Specifically, we show that, for any fixed finite field
$\F_q$, error fraction $\delta\in (0,1-1/q)$ satisfying $1-H_q(\delta)\le
\frac12$ and small $\epsilon>0$, with high probability a random Euclidean
self-orthogonal code over $\F_q$ of rate $1-H_q(\delta)-\epsilon$ is $(\delta,
O(1/\epsilon))$-list-decodable. This generalizes the result of linear codes to
Euclidean self-orthogonal codes. In addition, we extend the result to list
decoding {\it symplectic dual-containing} codes by showing that the
list-decodability of random symplectic dual-containing codes achieves the
quantum Gilbert-Varshamov bound as well. This implies that list-decodability of
quantum stabilizer codes can achieve the quantum Gilbert-Varshamov bound.
  The counting argument on self-orthogonal codes is an important ingredient to
prove our result.
