The generator matrix

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

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+9x^32+28x^33+42x^34+56x^35+50x^36+36x^37+32x^38+16x^39+34x^40+36x^41+42x^42+56x^43+28x^44+28x^45+6x^46+2x^48+4x^50+2x^52+2x^54+2x^56

The gray image is a linear code over GF(2) with n=78, k=9 and d=32.
This code was found by Heurico 1.16 in 0.015 seconds.