The generator matrix

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

generates a code of length 39 over Z2[X]/(X^2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+24x^32+54x^33+75x^34+96x^35+94x^36+86x^37+83x^38+76x^39+70x^40+62x^41+64x^42+72x^43+48x^44+42x^45+28x^46+12x^47+17x^48+12x^49+5x^50+2x^52+1x^54

The gray image is a linear code over GF(2) with n=78, k=10 and d=32.
This code was found by Heurico 1.16 in 0.0799 seconds.