Codes over F4, Jacobi forms and Hilbert-Siegel modular forms over Q(5)

We study codes over a finite field F4. We relate self-dual codes over F4 to real 5-modular lattices and to self-dual codes over F2 via a Gray map. We construct Jacobi forms over Q(5) from the complete weight enumerators of self-dual codes over F4. Furthermore, we relate Hilbert-Siegel forms to the joint weight enumerators of self-dual codes over F4.