gap> mat := [[0,1,0,0],[1,0,0,0],[0,0,0,1],[0,0,1,0]]*Z(16)^0;
[ [ 0*Z(2), Z(2)^0, 0*Z(2), 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), Z(2)^0, 0*Z(2) ] ]
gap> form := BilinearFormByMatrix(mat,GF(16));
< bilinear form >
gap> phi := PolarityOfProjectiveSpace(form);
<polarity of PG(3, GF(2^4)), >