Eisenstein lattices, Galois rings, and theta series

The Shrikhande graph is classically described in terms of a Galois ring of order 16 viewed as the Eisenstein integers modulo 4. Codes over that ring (but for a different weight) give rise to Eisenstein lattices, the theta series of which is expressed as a polynomial into three special theta series. As a special case the theta series of a lattice obtained by the complex Construction B from quaternary codes is derived.