The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X X 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X X X 0 0 0 0 0 0 0 X X X X X 0 X 0 0 0 1 1
0 X 0 0 0 X X X 0 0 0 X 0 X X X 0 0 0 X 0 X X X 0 0 0 X X 0 X X 0 X X 0 0 X X 0 0 X 0 X X X 0 0 0 X 0 X X X 0 0 X X 0 X X 0 X X X X 0 0 0 0 0 0 0 X X X X 0 0 0 X
0 0 X 0 X X X 0 0 0 X X X X 0 0 0 0 X X X X 0 0 0 0 X X 0 X X 0 0 0 X X 0 0 X X X X X X 0 0 0 0 X X X X 0 0 0 X X 0 X X 0 0 0 0 X X X X 0 0 0 X X X X X X X X 0 0
0 0 0 X X 0 X X 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 X X 0 0 0 X X X 0 X 0 X X 0 X X 0 0 X X 0 0 X X 0 0 X X 0 X X 0 0 0 X X 0 0 X X 0 0 X X 0 X X 0 0 0 X X 0 X 0 X
generates a code of length 81 over Z2[X]/(X^2) who´s minimum homogenous weight is 82.
Homogenous weight enumerator: w(x)=1x^0+14x^82+13x^84+2x^86+1x^88+1x^92
The gray image is a linear code over GF(2) with n=162, k=5 and d=82.
As d=82 is an upper bound for linear (162,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.0928 seconds.