  We show that any ternary Euclidean (resp.\ quaternary Hermitian) linear
complementary dual $[n,k]$ code contains a Euclidean (resp.\ Hermitian) linear
complementary dual $[n,k-1]$ subcode for $2 \le k \le n$. As a consequence, we
derive a bound on the largest minimum weights among ternary Euclidean linear
complementary dual codes and quaternary Hermitian linear complementary dual
codes.
