gap> mat := [[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]]*Z(8)^0;
[ [ 0*Z(2), 0*Z(2), Z(2)^0, 0*Z(2) ], [ 0*Z(2), 0*Z(2), 0*Z(2), Z(2)^0 ],
[ Z(2)^0, 0*Z(2), 0*Z(2), 0*Z(2) ], [ 0*Z(2), Z(2)^0, 0*Z(2), 0*Z(2) ] ]
gap> phi := PolarityOfProjectiveSpace(mat,GF(8));
<polarity of PG(3, GF(2^3)), >
gap> IsSymplecticPolarityOfProjectiveSpace(phi);
true