Let $R$ be a (commutative) local Artinian ring, with an algebraically closed residue field $k$. I am interested in the set $L_n(R)$ of isomorphism classes of $R$-modules of length $n$.

If $R$ is a $k$-algebra, this is a very classical subject. The set $\text{mod}_R^n$ of $R$-module structures on a fixed $k$-vector space of dimension $n$ has a natural structure of an affine $k$-scheme, and $L_n(R)$ can be viewed as the set of orbits of $GL_n(k)$ on $\text{mod}_R^n$. This has been exploited very frequently in the representation theory of Artin algebras.

I feel like the following question would be known to the right people, but could not find a satisfying reference:

Has the set $L_n(R)$ been studied in this general setting? I am more interested in geometric approaches, but any references would be welcome.

(The only remotely relevant reference I could find is this paper by Bjorn Poonen on moduli space of commutative algebras of finite rank over a commutative base).