  Let $F$ be a field with cardinality $p^\ell$ and $0\neq \lambda\in F$, and
$0\le h<\ell$. Extending Euclidean and Hermitian inner products, Fan and Zhang
introduced Galois $p^h$-inner product (DCC, vol.84, pp.473-492). In this paper,
we characterize the structure of $2$-quasi $\lambda$-constacyclic codes over
$F$; and exhibit necessary and sufficient conditions for $2$-quasi
$\lambda$-constacyclic codes being Galois self-dual. With the help of a
technique developed in this paper, we prove that, when $\ell$ is even, the
Hermitian self-dual $2$-quasi $\lambda$-constacyclic codes are asymptotically
good if and only if $\lambda^{1+p^{\ell/2}}=1$. And, when
$p^\ell\,{\not\equiv}\,3~({\rm mod}~4)$, the Euclidean self-dual $2$-quasi
$\lambda$-constacyclic codes are asymptotically good if and only if
$\lambda^{2}=1$.
