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In this work, we give a new technique for constructing self-dual codes overcommutative Frobenius rings using $\lambda$-circulant matrices. The newconstruction was derived as a modification of the well-known four circulantconstruction of self-dual codes. Applying this technique together with thebuilding-up construction, we construct singly-even binary self-dual codes oflengths 56, 58, 64, 80 and 92 that were not known in the literature before.Singly-even self-dual codes of length 80 with $\beta\in\{2,4,5,6,8\}$ in theirweight enumerators are constructed for the first time in the literature.

New binary self-dual codes of lengths 56, 58, 64, 80 and 92 from a modification of the four circulant construction