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

generates a code of length 81 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+7x^78+16x^79+23x^80+32x^81+23x^82+16x^83+7x^84+1x^94+1x^100+1x^130

The gray image is a linear code over GF(2) with n=162, k=7 and d=78.
This code was found by Heurico 1.16 in 0.078 seconds.