Direct computation of matrix representations of Hodge operators (without using KappaLib)

Bin[k_]:=Module[{t},
t={{1,2},{1,3},{1,4},{3,4},{4,2},{2,3}};
t[[k]]
];

Bin[2]

L[g_] :=Module[{}, 
Table[
Sum[g[[Bin[i][[1]]]][[a]]g[[Bin[i][[2]]]][[b]]Signature[{a,b,Bin[j][[1]],Bin[j][[2]]}],{a,1,4},{b,1,4}],{i,1,6},{j,1,6}]
]

g = DiagonalMatrix[{1,1,1,1}];
L[g]//MatrixForm

g = DiagonalMatrix[{1,-1,-1,1}];
L[g]//MatrixForm