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Let $K=Q(\sqrt{-\ell})$ be an imaginary quadratic field with ring of integers$\O_K$, where $\ell$ is a square free integer such that $\ell\equiv 3 \mod 4$and $C=[n, k]$ be a linear code defined over $\O_K/2\O_K$. The level $\ell$theta function $\Th_{\L_{\ell} (C)} $ of $C$ is defined on the lattice$\L_{\ell} (C):= \set {x \in \O_K^n : \rho_\ell (x) \in C}$, where$\rho_{\ell}:\O_K \rightarrow \O_K/2\O_K$ is the natural projection. In thispaper, we prove that: % i) for any $\ell, \ell^\prime$ such that $\ell \leq\ell^\prime$, $\Th_{\Lambda_\ell}(q)$ and $\Th_{\Lambda_{\ell^\prime}}(q)$ havethe same coefficients up to $q^{\frac {\ell+1}{4}}$, % ii) for $\ell \geq \frac{2(n+1)(n+2)}{n} -1$, $\Th_{\L_{\ell}} (C)$ determines the code $C$ uniquely, %iii) for $\ell < \frac {2(n+1)(n+2)}{n} -1$ there is a positive dimensionalfamily of symmetrized weight enumerator polynomials corresponding to$\Th_{\La_\ell}(C)$.

Codes over rings of size four, Hermitian lattices, and corresponding theta functions