The generator matrix

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

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+97x^28+252x^30+537x^32+824x^34+1100x^36+1258x^38+1358x^40+1032x^42+926x^44+424x^46+290x^48+48x^50+36x^52+2x^54+6x^56+1x^60

The gray image is a linear code over GF(2) with n=78, k=13 and d=28.
This code was found by Heurico 1.16 in 4.39 seconds.