The generator matrix

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

generates a code of length 72 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+57x^68+54x^70+62x^72+30x^74+27x^76+10x^78+12x^80+2x^82+1x^136

The gray image is a linear code over GF(2) with n=144, k=8 and d=68.
This code was found by Heurico 1.16 in 0.109 seconds.