I want to calculate the number of unrepeated Jordan canonical forms of n * n matrices consisting of 0 and 1 How to speed up this code

sol4=Flatten[Inactive[Table][Table[x[(i-1) 4+j],{i,1,4},{j,1,4}],Sequence@@Table[{x[i],0,1},{i,1,16}]]//Activate,15];GatherBy[sol4,(JordanDecomposition[#1][[2]])&]//Length