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 X X 0 X X X X X X X X X X X X X X
0 X 0 0 0 0 0 0 0 X X X X X X X 0 0 0 0 0 0 X X X X X 0 X 0 X 0 X 0 X 0 X 0 X 0 X
0 0 X 0 0 0 X X X X X 0 X X 0 0 0 0 0 0 X X X X 0 0 0 0 0 X X X X 0 0 X X X X 0 0
0 0 0 X 0 X X X 0 0 0 0 X X X X 0 0 X X X X 0 0 0 0 0 X X X X 0 0 X X X X 0 0 0 0
0 0 0 0 X X 0 X X 0 X X X 0 0 X 0 X X 0 0 X 0 X X 0 0 X 0 0 X 0 X 0 X X 0 X 0 X 0
generates a code of length 41 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.
Homogenous weight enumerator: w(x)=1x^0+48x^40+8x^44+5x^48+2x^56
The gray image is a linear code over GF(2) with n=82, k=6 and d=40.
As d=40 is an upper bound for linear (82,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.417 seconds.