We suggest a Jacobi form over a number field $\mathbb{Q}(\sqrt{5},i)$; for obtaining this, we use a linear code $C$ over $R:={\mathbb{F}}_4+u{\mathbb{F}}_4$, where $u^2=0$. We introduce MacWilliams identities for both complete weight enumerator and symmetrized weight enumerator in higher genus $g\ge 1$ of a linear code over $R$. Finally, we give invariants via a self-dual code of even length over $R$.