The generator matrix

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

generates a code of length 39 over Z2[X]/(X^2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+84x^31+203x^32+236x^33+212x^34+252x^35+331x^36+296x^37+275x^38+326x^39+337x^40+284x^41+269x^42+274x^43+231x^44+192x^45+129x^46+86x^47+47x^48+16x^49+10x^50+2x^51+2x^52+1x^66

The gray image is a linear code over GF(2) with n=78, k=12 and d=31.
This code was found by Heurico 1.16 in 9.01 seconds.