The generator matrix

1 0 0 0 0 0 1 1 1 X 1 1 0 0 0 1 1 1 X X 0 1 0 X 1 1 1 1 1 1 X X X 1 1 1 0 1 1
0 1 0 0 0 0 0 0 0 0 0 0 X 1 1 1 X+1 1 1 1 X X+1 1 1 X X+1 1 X+1 X+1 1 X X 1 X+1 1 1 X 0 0
0 0 1 0 0 0 0 0 X X 1 1 1 X 1 0 0 X+1 1 X 1 X X 1 1 1 1 0 X+1 X 0 1 X 1 0 X X X+1 0
0 0 0 1 0 0 1 X 1 1 0 X+1 1 1 X X+1 0 0 0 1 X+1 0 X 1 1 1 X X+1 1 1 1 X X+1 0 1 0 1 0 0
0 0 0 0 1 0 1 X+1 0 1 X X+1 1 1 X 1 X X+1 X+1 X 0 X+1 X+1 0 X X+1 X X X 0 X+1 X+1 0 0 0 X+1 0 0 0
0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 X X+1 1 X+1 1 X 1 1 X X+1 0 X 0 0 X X+1 X+1 X 0 0 1 X+1 0 X+1 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+60x^30+78x^31+157x^32+244x^33+243x^34+252x^35+266x^36+270x^37+316x^38+334x^39+268x^40+310x^41+312x^42+282x^43+204x^44+186x^45+135x^46+76x^47+62x^48+14x^49+21x^50+2x^51+2x^52+1x^62

The gray image is a linear code over GF(2) with n=78, k=12 and d=30.
This code was found by Heurico 1.10 in 0.422 seconds.