The generator matrix

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

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+18x^34+18x^35+29x^36+44x^37+28x^38+26x^39+18x^40+16x^41+9x^42+14x^43+10x^44+4x^45+5x^46+6x^47+5x^48+1x^50+1x^52+3x^54

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 0.015 seconds.