  We study some properties of the lattices defined as the kernel of the map
$(a_1,\ldots, a_{q-1}) \mapsto \prod (1-c_ix)^{a_i} \in
(\mathbb{F}_q[x]/(x^e))^*$, where $\mathbb{F}_q^* = \{c_1,\ldots,c_{q-1}\}$.
