Dear Katsushi Waki,

to compute the cohomology of a pc group G and a module M, the
generating matrices in M must correspond to the action of the
elements in Pcgs(G). In your example you can achieve this by:

gap> g := GL(2,2);;
gap> orb := Orbit(g,One(GF(2))*[1,0],OnLines);;
gap> iso_pgl := OperationHomomorphism( g, orb, OnLines );;
gap> pgl := Image( iso_pgl );;
gap> iso_g := IsomorphismPcGroup(pgl);; 
gap> G := Image(iso_g);;
gap> mats := List(Pcgs(G), x -> PreImagesRepresentative(iso_g, x) );;
gap> mats := List(mats, x -> PreImagesRepresentative(iso_pgl, x) );;
gap> M := GModuleByMats( mats, GF(2) );;

gap> TwoCoboundaries( G, M );
[ [ Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ],
  [ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ] ]

gap> TwoCocycles( G, M );
[ [ Z(2)^0, 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ],
  [ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ] ]

gap> TwoCohomology( G, M ).cohom;
ZeroMapping( <vector space of dimension 2 over GF(2)>, ( GF(2)^0 ) )

Best wishes,
           Bettina