The generator matrix

 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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  X  X  1  1  X  1  1  1  1  0
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  0  0  X  X  0  X  0  X  0  X  X  X  0  X  X  X  X  X  X  0  X  0  X  0  0  X  X  X  X
 0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  X  X  0  0  X  X  X  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  X  0  0  X  X  0  0  0  X  X  X  0  X  0  0  X  X  0  0  0
 0  0  0  X  0  0  0  X  X  X  X  X  0  X  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  X  X  X  X  X  X  0  0  X  0  X  0  0  X  X  0  0  X  X  0  0  0  X  0  0  0  X  X  0  X  0  X  X
 0  0  0  0  X  0  X  X  X  0  0  0  0  X  X  X  X  0  0  0  X  X  X  X  X  X  0  0  0  0  X  X  0  0  X  X  X  X  0  0  0  0  0  0  X  X  X  X  X  X  0  X  X  0  X  X  X  X  X  0  0  0  X  X  0  0  0  0  X
 0  0  0  0  0  X  X  0  X  X  0  X  X  X  0  0  X  0  X  X  X  0  0  X  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  0  X  X  X  0  0  0  0  0  0  X  X  0  0  X  X  X  0  X  X  X  X  0  0  X  X  X

generates a code of length 69 over Z2[X]/(X^2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+12x^65+15x^66+15x^68+40x^69+15x^70+15x^72+12x^73+1x^74+1x^76+1x^126

The gray image is a linear code over GF(2) with n=138, k=7 and d=65.
This code was found by Heurico 1.16 in 0.141 seconds.