  Let ${\bf A}={\bf A}_{n,m,k}$ be a random $n\times m$ matrix over
$\mathbf{GF}_2$ wher each column consists of $k$ randomly chosen ones. Let $M$
be an arbirary fixed binary matroid. We show that if $m/n$ and $k$ are
sufficiently large then as $n\to\infty$ the binary matroid induced by {\bf A}
contains $M$ as a minor.
