Yoshitake Matsumoto maintains some <a href="http://www-imai.is.s.u-tokyo.ac.jp/~ymatsu/matroid/index.html">databases of matroids</a>.  Gordon Royle also has a database of matroids that might contain some data not in Matsumoto's database, but I can't seem to find it on <a href="http://staffhome.ecm.uwa.edu.au/~00013890/">his webpage</a>.  The URL in <a href="http://arxiv.org/abs/math/0702316">his paper with Mayhew</a> does not seem to work any more.  You might have to contact Royle or Mayhew.