The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  X  X  1  X  1  1  X  1  1  X  0  X
 0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  0  0  X  X  0  0  0  X  0  X  X  X  X  0  X  0  X  X  0  0  X  0  X
 0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  0  0  0  0  X  X  X  X  0  0  0  X  0  X  0  X  X  0  X  0  X
 0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  0  X  X  0  X  0  X  X  X  X  X  0  0  0  X  0  X  0  0  0  X  X
 0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  X  0  0  X  0  0  0  0  0  X  X  0  X  X  0  X  X  X  0  0
 0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  X  0  0  X  X  X  X  X  X  X  0  0  X  0  X  X  X  X  0  0  0  0  X
 0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  X  X  0  0  0  0  X  X  0  0  X  X  0  X  0  X  X  X  X  0  0  X  0
 0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  0  X  0  0  X  X  X  X  0  X  0  X  0  X  X  0  X  0  X  X  0  X
 0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0  0  0  X  0  0  X  X  0  X  0  X  X  0  0  0  X  0  0  0  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+166x^32+36x^34+137x^36+132x^38+283x^40+76x^42+91x^44+12x^46+77x^48+11x^52+1x^56+1x^60

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 45.8 seconds.