  We extend the computations in [AGM4] to find the mod 2 homology in degree 1
of a congruence subgroup Gamma of SL(4,Z) with coefficients in the sharbly
complex, along with the action of the Hecke algebra. This homology group is
closely related to the cohomology of Gamma with F_2 coefficients in the top
cuspidal degree. These computations require a modification of the algorithm to
compute the action of the Hecke operators, whose previous versions required
division by 2. We verify experimentally that every mod 2 Hecke eigenclass found
appears to have an attached Galois representation, giving evidence for a
conjecture in [AGM4]. Our method of computation was justified in [AGM5].
