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 sage: g=libgap.Group(map(lambda s: libgap.PermList(s.get_perm()), Gautgens))

will give you the underlying permutation group. It has 1 orbit in its natural action (on 8 points):

 sage: g.Orbits()
 [ [ 1, 2, 5, 3, 6, 4, 7, 8 ] ]

You can convert it into a matrix group acting on GF(4)^8.

 sage: mg=libgap.Group(map(lambda s: libgap.PermutationMat(s,8,libgap.GF(4)), g.GeneratorsOfGroup()))

Now you can compute orbits on vectors (see e.g. code in graphs/generators/ for details); however, you might want to make sure that GAP's GF(4) is created in a compatible way.