In a series of papers, Ash, Gunnells and McConnell have studied cohomology groups for congruence subgroups Gamma of SL(4,Z), and have verified experimentally that Hecke eigenclasses for these cohomology groups seem to have attached Galois representations.  We will report especially on the latest paper, which relates to the cohomology of Gamma with F_2 coefficients in the top cuspidal degree.  The Galois representations we find come from Dirichlet characters, or from classical cusp forms in characteristic zero of weights 2, 3 or 4.  The talk will include background on how we perform the topological computations, using a cell complex which lives naturally in the space of 4-dimensional lattices.