Is there a computer programm that can list all finite dimensional commutative local (nonsemisimple) k-algebras $K<x_1,x_2,...,x_n>/I$ over a finite field k (of order $q$) with $J^l=0$ for a given $q, n$ and $l$ , when $J$ denotes the Jacobson radical of such an algebra?

Is there an estimate how many there are (up to isomorphism or not).