The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  X  1  1  X  X  1  0  1  0  1  1  X  1  1  1  1  1  1  0  0  1  1  0  X  X  1
 0  1  0  1  0  1  1  0  0  1 X+1  1  X  1  0  1  1  1  X  1 X+1  0  0 X+1  1  1  0  X  X X+1  0  X  X  X  1  X  1  1  0
 0  0  1  1  1  0  1  0  1  1  0  X  1  1  0 X+1  1 X+1  1  0  0  1  X X+1  X  1  X  1  1  0  0  1  1  X  X  1 X+1 X+1  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  X  0  X  0  0  X  X  X  0  0  0  X  X  X  X  0  X  X  X  0
 0  0  0  0  X  0  0  0  0  0  X  X  X  0  X  0  X  0  0  X  0  0  X  X  0  0  X  X  0  0  X  0  0  X  X  0  X  X  0
 0  0  0  0  0  X  0  0  0  0  X  0  0  X  X  X  0  X  0  X  0  0  0  0  0  X  X  X  X  0  X  0  0  0  X  0  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  X  0  X  X  0  X  X  X  0  0  X  X  0  0  0  0  X  X  X  X  X  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  X  X  0  X  X  0  0  0  X  X  X  X  0  X  0  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  X  X  X  X  X  0  0  0  0  X  X  0  0  X  X  X  X  0  0  X  X  X  X  0
 0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  0  X  X  X  X  0  0  0  X  X  0  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+95x^28+12x^29+115x^30+146x^31+312x^32+304x^33+346x^34+482x^35+561x^36+688x^37+624x^38+780x^39+603x^40+760x^41+572x^42+508x^43+377x^44+260x^45+289x^46+130x^47+91x^48+24x^49+90x^50+2x^51+7x^52+11x^54+1x^56+1x^70

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 4.46 seconds.