Weight Enumerators of Codes Over 𝔽<sub>2</sub> and Over ℤ<sub>4</sub>

In this study we focus on symmetrized weight enumerators of pairs of Type II codes over the finite field F2 and the ring Z4. These pairs have been examined as invariants for a specified group. In particular, we concentrate on the scenarios where the space of the invariant ring is of degree 8 and 16. Our findings show that, the ring produced by the symmetrized weight enumerators precisely matches with the invariant ring of the designated group.