ClearAll["Global`*"]
set1 = Tuples[Table[i, {i, 1, 3}], 3];
set2 = Tuples[Table[Tuples[{1, -1}, 3], {3}]];
w[i_, j_] := Product[set2[[i]][[k]][[set1[[j]][[k]]]], {k, 1, 3}];
set3 = DeleteDuplicates[
  Table[Table[w[i, j], {j, 1, Length[set1]}], {i, 1,
    Length[set2]}]]; "";
set4 = Take[Reverse[Sort[set3]], Length[set3]/2]; "";
set5 = {{ConstantArray[1, 27]}};
set6 = {#} & /@ Complement[set4, {ConstantArray[1, 27]}];
f[set6_, {i_, set5_}] :=
 Module[{S1, S2}, S1 = Join @@@ Tuples[{set6, set5}];
  S2 = Pick[DeleteDuplicatesBy[Sort]@S1,
    MatrixRank[#] == i & /@ DeleteDuplicatesBy[Sort]@S1];
  {i + 1, S2}]
biglist = Last@Nest[f[set6, #] &, {2, set5}, *ITERATIONS*];