On classifying Minkowskian sublattices

Let $\mathrm{\Lambda }$ be a lattice in an $n$-dimensional Euclidean space $E$ and let ${\mathrm{\Lambda }}^{\mathrm{\prime }}$ be a Minkowskian sublattice of $\mathrm{\Lambda }$, that is, a sublattice having a basis made of representatives for the Minkowski successive minima of $\mathrm{\Lambda }$. We extend the classification of possible $\mathbb{Z}\mathrm{/}d\mathbb{Z}$-codes of the quotients $\mathrm{\Lambda }\mathrm{/}{\mathrm{\Lambda }}^{\mathrm{\prime }}$ to dimension~$9$, where $d\mathbb{Z}$ is the annihilator of $\mathrm{\Lambda }\mathrm{/}{\mathrm{\Lambda }}^{\mathrm{\prime }}$.