The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  1  X  1  1  X  X  0  X  1  1  1  1  1  1  1  1  X  1  1  1  0  1  1  1
 0  1  0  0  0  1  1  1  X  0 X+1 X+1  1  1  X  1  1 X+1 X+1  1  X  1  0  X  X  X X+1  X  X  0 X+1  0  1  X  X  1  1 X+1  X
 0  0  1  0  1  1  0  1  0 X+1 X+1  X  X X+1  1  1  X  0  X  0  1 X+1  0 X+1 X+1  1 X+1  0  1  X  1  X  1  1  X  1 X+1  1  X
 0  0  0  1  1  0  1  1  1  0  1  X X+1  0  1 X+1  X  X  X  1  X  X  1 X+1  1 X+1  0 X+1  X X+1  1  1 X+1  X  0  X  0 X+1 X+1
 0  0  0  0  X  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  0  X  X  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  X  0  X  0  0  0  X  0  X  0  X  X  0  X  X  0  X  0  X  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  0  X  0  0  0  X  X  X  X  0  0  X  X  0  0  X  0  0  X  0  X  0
 0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  X  X  X  X  X  0  X  X  0  X  X  0  0  0  0  0  X  0  0  0  0  0  X  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+72x^31+135x^32+224x^33+241x^34+254x^35+300x^36+286x^37+289x^38+322x^39+329x^40+374x^41+296x^42+294x^43+206x^44+122x^45+119x^46+78x^47+44x^48+18x^49+23x^50+4x^51+6x^52+1x^54+3x^56

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 1.11 seconds.