Let K be a field with at least 19 elements. It is proved that any subgroup of GL(4, K) generated by a pair of 2-tori contains unipotent elements of rank 1 or 2. Taking into account previous papers of N. A. Vavilov and the author, this result is valid for any general linear group. It is one of the first steps in studying subgroups generated by a pair of microweight tori in Chevalley groups.