The AutoKron can't determine the cohomology of $\text{Gr}_4(\mathbb{R}^{8,2})$.
There are 6 possibilities.
Here are their Poincaré polynomials:
$$x^{16} y^{6} + x^{15} y^{6} + x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + 4 x^{12} y^{5} + x^{12} y^{4} + 2 x^{11} y^{5} + 3 x^{11} y^{4} + 7 x^{10} y^{4} + 6 x^{9} y^{4} + x^{9} y^{3} + 5 x^{8} y^{4} + 3 x^{8} y^{3} + 2 x^{7} y^{4} + 4 x^{7} y^{3} + x^{7} y^{2} + 4 x^{6} y^{3} + 3 x^{6} y^{2} + 2 x^{5} y^{3} + 3 x^{5} y^{2} + 5 x^{4} y^{2} + 3 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$
$$x^{16} y^{6} + x^{15} y^{6} + x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + 4 x^{12} y^{5} + x^{12} y^{4} + 2 x^{11} y^{5} + 3 x^{11} y^{4} + 7 x^{10} y^{4} + 6 x^{9} y^{4} + x^{9} y^{3} + 4 x^{8} y^{4} + 4 x^{8} y^{3} + 2 x^{7} y^{4} + 5 x^{7} y^{3} + 4 x^{6} y^{3} + 3 x^{6} y^{2} + 2 x^{5} y^{3} + 3 x^{5} y^{2} + 5 x^{4} y^{2} + 3 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$
$$x^{16} y^{6} + x^{15} y^{6} + x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + 4 x^{12} y^{5} + x^{12} y^{4} + 2 x^{11} y^{5} + 3 x^{11} y^{4} + 7 x^{10} y^{4} + 6 x^{9} y^{4} + x^{9} y^{3} + 5 x^{8} y^{4} + 3 x^{8} y^{3} + x^{7} y^{4} + 5 x^{7} y^{3} + x^{7} y^{2} + 5 x^{6} y^{3} + 2 x^{6} y^{2} + 2 x^{5} y^{3} + 3 x^{5} y^{2} + 5 x^{4} y^{2} + 3 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$
$$x^{16} y^{6} + x^{15} y^{6} + x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + 4 x^{12} y^{5} + x^{12} y^{4} + 2 x^{11} y^{5} + 3 x^{11} y^{4} + 7 x^{10} y^{4} + 6 x^{9} y^{4} + x^{9} y^{3} + 4 x^{8} y^{4} + 4 x^{8} y^{3} + x^{7} y^{4} + 6 x^{7} y^{3} + 5 x^{6} y^{3} + 2 x^{6} y^{2} + 2 x^{5} y^{3} + 3 x^{5} y^{2} + 5 x^{4} y^{2} + 3 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$
$$x^{16} y^{6} + x^{15} y^{6} + x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + 4 x^{12} y^{5} + x^{12} y^{4} + 2 x^{11} y^{5} + 3 x^{11} y^{4} + 7 x^{10} y^{4} + 6 x^{9} y^{4} + x^{9} y^{3} + 5 x^{8} y^{4} + 3 x^{8} y^{3} + 6 x^{7} y^{3} + x^{7} y^{2} + 6 x^{6} y^{3} + x^{6} y^{2} + 2 x^{5} y^{3} + 3 x^{5} y^{2} + 5 x^{4} y^{2} + 3 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$
$$x^{16} y^{6} + x^{15} y^{6} + x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + 4 x^{12} y^{5} + x^{12} y^{4} + 2 x^{11} y^{5} + 3 x^{11} y^{4} + 7 x^{10} y^{4} + 6 x^{9} y^{4} + x^{9} y^{3} + 4 x^{8} y^{4} + 4 x^{8} y^{3} + 7 x^{7} y^{3} + 6 x^{6} y^{3} + x^{6} y^{2} + 2 x^{5} y^{3} + 3 x^{5} y^{2} + 5 x^{4} y^{2} + 3 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$
Here are the corresponding generator grids to these 6 possibilities: