  We extend the computations in our prior work to find the cohomology in degree
five of a congruence subgroup Gamma of SL_4(Z) with coefficients in Sym^g(K^4),
twisted by a nebentype character eta, along with the action of the Hecke
algebra. This is the top cuspidal degree. In this paper we take K to be a
finite field of large characteristic, as a proxy for the complex numbers. For
each Hecke eigenclass found, we produce the unique Galois representation that
appears to be attached to it. The computations require modifications to our
previous algorithms to accommodate the fact that the coefficients are not
one-dimensional.
