Non-finite-field representations of color algebras

Construct representations of $\mathfrak{E}_n(\{2,3\})$ for some $n>4$ that are not finite-field representations, and in particular determine whether such algebras have representations over a number of points that is neither a prime nor a prime power.

Background

For $n\geq 4$, the paper states that all currently known representations of the color algebras are finite-field representations. This leaves open whether the apparent dominance of the finite-field method reflects a genuine structural restriction or merely the limits of existing constructions.

The question includes the more specific possibility of representations whose underlying set has cardinality that is not a prime or a prime power.