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.