On additive modular bivariate codes over F4F4

Additive multivariate codes over F4F4 (the Galois field with 4 elements) are a natural extension of additive cyclic and abelian codes. A complete description of such codes when the length is odd was presented in [11]. In this paper we study some properties of this family of codes in the case when the length is even (modular case) and the number of variables is two (bivariate codes).