Weighing Matrices and Self-Orthogonal Quaternary Codes

We consider families of linear self-orthogonal and self-dual codes over the ring \({Z}_4\), which are generated by weighing matrices \(W(n, k)\) with \(k \equiv 0 \pmod{4}\), whose entries are interpreted as elements of the ring \({Z}_4\). We obtain binary formally self-dual codes of minimal Hamming distance 4 by applying the Gray map to the quaternary codes generated by \(W(n, 4)\).