  In this work, we define a modification of a bordered construction for
self-dual codes which utilises $\lambda$-circulant matrices. We provide the
necessary conditions for the construction to produce self-dual codes over
finite commutative Frobenius rings of characteristic 2. Using the modified
construction together with the neighbour construction, we construct many binary
self-dual codes of lengths 54, 68, 82 and 94 with weight enumerators that have
previously not been known to exist.
