The generator matrix

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

generates a code of length 39 over Z2[X]/(X^2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+55x^30+68x^31+193x^32+202x^33+218x^34+296x^35+254x^36+294x^37+336x^38+320x^39+282x^40+334x^41+255x^42+284x^43+218x^44+170x^45+137x^46+52x^47+68x^48+24x^49+22x^50+4x^51+8x^52+1x^58

The gray image is a linear code over GF(2) with n=78, k=12 and d=30.
This code was found by Heurico 1.16 in 1.09 seconds.