  In this paper we describe a parallel algorithm for generating all
non-isomorphic rank $3$ simple matroids with a given multiplicity vector. We
apply our implementation in the HPC version of GAP to generate all rank $3$
simple matroids with at most $14$ atoms and a splitting characteristic
polynomial. We have stored the resulting matroids alongside with various useful
invariants in a publicly available, ArangoDB-powered database. As a byproduct
we show that the smallest divisionally free rank $3$ arrangement which is not
inductively free has $14$ hyperplanes and exists in all characteristics
distinct from $2$ and $5$. Another database query proves that Terao's freeness
conjecture is true for rank $3$ arrangements with $14$ hyperplanes in any
characteristic.
