The generator matrix

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

generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+33x^64+26x^65+42x^66+44x^67+25x^68+28x^69+13x^70+16x^71+2x^72+4x^73+2x^74+1x^76+5x^78+2x^80+4x^81+2x^82+4x^83+2x^89

The gray image is a linear code over GF(2) with n=136, k=8 and d=64.
This code was found by Heurico 1.16 in 0.0558 seconds.