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  X  1  X  1  1  X  1  1  1  1  X  1  1  1  X  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  0  X  0  X  X  X  0  X  X  X  X
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  X  0  X  X  X  0  0  X  0  X  X  X  0  0  X
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  X  X  X  0  X  X  X  0  0  X  0  X  X  X  0  0  X  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  0  X  X  X  0  0  X  X  X  0  0  0  0  0  0  X  0  X
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  X  0  X  X  0  X  0  X  X  0  0  0  0  0  X  0  X  X  X  X  0  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  X  X  X  X  0  X  X  0  0  X  0  0  X  0  X  X  0  0  0  0  X  X  0
 0  0  0  0  0  0  0  X  0  0  0  X  0  0  0  0  X  X  0  X  0  0  0  X  X  0  X  X  X  0  X  0  X  0  0  0  X  X  0
 0  0  0  0  0  0  0  0  X  0  0  X  0  0  0  X  0  0  X  0  X  0  0  X  0  X  0  X  X  X  X  0  0  X  X  X  0  X  X
 0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  0  0  0  X  0  0  X  X  0  0  0  X  0  0  0  X  X  X  0  X  0  X  X
 0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  X  X  X  X  X  0  X  X  X  X  0  X  X  0  0  0  X  0  0  0  0  X

generates a code of length 39 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+157x^28+333x^32+64x^34+704x^36+640x^38+1142x^40+320x^42+459x^44+214x^48+55x^52+6x^56+1x^68

The gray image is a linear code over GF(2) with n=78, k=12 and d=28.
This code was found by Heurico 1.16 in 1.87 seconds.