We introduce codes over the ring We relate self-dual codes over this ring to quaternionic unimodular lattices and to self-dual codes over via a gray map. We study a connection between the complete weight enumerators of codes over the quaternionic ring _2m and Jacobi forms over the half-space of quaternions. This motivates us to construct an algebra homomorphism from a certain invariant polynomial ring, where the complete weight enumerators belong, to the ring of Jacobi forms over the quaternions. Higher genus modular forms over the quaternions are also constructed using joint weight enumerators of codes.