  In this work, we give three new techniques for constructing Hermitian
self-dual codes over commutative Frobenius rings with a non-trivial involutory
automorphism using $\lambda$-circulant matrices. The new constructions are
derived as modifications of various well-known circulant constructions of
self-dual codes. Applying these constructions together with the building-up
construction, we construct many new best known quaternary Hermitian self-dual
codes of lengths 26, 32, 36, 38 and 40.
