The generator matrix

 1  0  0  1  1  1  X  1  1  X  1  X  1  0  1  1  1  1  1  1  X  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  0  1 X+1  1  X X+1  1  0  0  1  1  X  X  X  0  0  1  1  X X+1  1  0  1 X+1  1  X  1 X+1 X+1  1  1  X X+1  0 X+1  X  0
 0  0  1  1 X+1  0 X+1  1 X+1  X  X  1  X  1  1 X+1 X+1  1  0  1 X+1  X X+1 X+1  X X+1  0  X  X  1  X  X  0  0  0  1 X+1  0  0  0
 0  0  0  X  X  X  0  0  0  X  X  X  0  X  X  0  X  0  X  X  X  X  X  X  0  0  0  X  0  0  X  0  X  0  X  X  0  0  0  X

generates a code of length 40 over Z2[X]/(X^2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+47x^38+47x^40+14x^42+14x^44+3x^46+1x^48+1x^64

The gray image is a linear code over GF(2) with n=80, k=7 and d=38.
As d=38 is an upper bound for linear (80,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.0127 seconds.