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 X X X X X X X 0 0 0 0 0 0 0 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 X 1 1 1 1 X 0 X X 0 0 X 0
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 X X X X 0 0 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 0 X 0 0 0 X X X X X X X 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 X X 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 0 X X X X 0 0 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 0 X X 0 0 X X 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 0 X X 0 0 X X X X 0 0
generates a code of length 80 over Z2[X]/(X^2) who´s minimum homogenous weight is 81.
Homogenous weight enumerator: w(x)=1x^0+16x^81+6x^82+6x^84+1x^86+1x^88+1x^94
The gray image is a linear code over GF(2) with n=160, k=5 and d=81.
As d=81 is an upper bound for linear (160,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.116 seconds.