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

generates a code of length 39 over Z2[X]/(X^2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+28x^34+54x^36+54x^38+52x^40+38x^42+16x^44+2x^46+3x^48+6x^50+1x^52+1x^68

The gray image is a linear code over GF(2) with n=78, k=8 and d=34.
This code was found by Heurico 1.16 in 3.26 seconds.