The generator matrix

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

generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+10x^65+18x^66+16x^67+26x^68+36x^69+12x^70+5x^72+2x^73+1x^94+1x^102

The gray image is a linear code over GF(2) with n=136, k=7 and d=65.
This code was found by Heurico 1.16 in 0.203 seconds.