The generator matrix

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

generates a code of length 79 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+30x^78+64x^79+30x^80+1x^94+1x^96+1x^126

The gray image is a linear code over GF(2) with n=158, k=7 and d=78.
As d=78 is an upper bound for linear (158,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.124 seconds.