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  X  X  0  X  X  0  X  0  0  0  X  0  0  0
 0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  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  X  X  X  0  0  X  0  0  0  0  X  X  0  0  X  X
 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  X  X  0  X  X  0  0  X  X  0  0  X  X  0
 0  0  0  0  X  X  0  X  X  0  X  X  X  0  0  X  0  X  X  0  0  X  X  0  0  X  X  0  0  0  X  X  X  X  0  0  0  0  X  X

generates a code of length 40 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+60x^40+2x^48+1x^64

The gray image is a linear code over GF(2) with n=80, k=6 and d=40.
As d=40 is an upper bound for linear (80,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 4.66 seconds.