The generator matrix
1 0 0 0 1 1 1 X 1 1 0 X 1 X 0 0 X 1 1 1 0 1 1 X X 1 X 1 1 1 1 1 1 1 1 1 1 1 0
0 1 0 0 0 0 0 X 1 X+1 1 1 X+1 1 X 1 1 X+1 X+1 0 X 1 0 X 1 1 1 1 X+1 X 0 0 1 0 1 0 X X+1 X
0 0 1 0 0 1 X+1 1 X+1 1 1 X 0 1 X 1 0 X X+1 X 1 X+1 0 1 X X+1 X 0 1 1 0 1 1 0 X X+1 0 0 1
0 0 0 1 1 1 0 1 X X+1 1 X+1 0 X+1 1 X X 1 X 0 1 X+1 X+1 X 0 1 X+1 1 X 1 X 1 X X X+1 1 X+1 1 X+1
0 0 0 0 X 0 0 X 0 0 X X X 0 X 0 X X X X 0 0 X X 0 X 0 0 0 X X X 0 0 0 0 0 0 X
0 0 0 0 0 X X X X X X 0 X X 0 0 X X 0 X X 0 X 0 X X 0 0 0 0 0 X X X X 0 X 0 X
generates a code of length 39 over Z2[X]/(X^2) who´s minimum homogenous weight is 33.
Homogenous weight enumerator: w(x)=1x^0+48x^33+118x^34+102x^35+61x^36+94x^37+115x^38+86x^39+33x^40+66x^41+95x^42+38x^43+29x^44+34x^45+49x^46+26x^47+2x^48+14x^49+7x^50+4x^51+2x^52
The gray image is a linear code over GF(2) with n=78, k=10 and d=33.
This code was found by Heurico 1.16 in 2.88 seconds.