Semimonomial transformation group

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I have a subgroup of the semimonomial transformation group which is implemented in Sage and would like to be able to use for example the Orbit-functions in GAP, any ideas of how to do this?

Below I compute the full automorphism group of a linear [8,5] code over GF(4), with its generators stored in the variable "Gautgens".

f.<w>=GF(4,'x')
G=matrix(f,[[1,0],[w,1]])
Gt=reduce(lambda x,y:x.tensor_product(y,subdivide=False),[G]*3)
C=LinearCode(Gt[range(3,8)])
Gautgens=C.automorphism_group_gens()[0]

What I would like to do is to use the Orbits-function in GAP to find the orbits of some vectors in GF(4)^8 (v1,v2,v3,...) under the action of the automorphism group above. That is, something like:

gap.Orbits(gap.Group(Gautgens),[v1,v2,v3,..],"On....")

But I don't know how to make the automorphism group a group in GAP.

An alternative solution for me would be to map the automorphism group to an isomorphic permutation group acting on points. That is I would number all the vectors in GF(4)^8 and the automorphism group would then act as a permutation group on this indexing.