The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  0  1  1  1  0  1  X  0  0  1  0  1  0  1  1  1  0  1  X  0  1  1  1  1  X  0
 0  1  0  1  0  1  1  0  0  1  1  1  1  X  X  X  1  1 X+1  1  0  0  X  1 X+1  0  X X+1 X+1  X  X  X  0 X+1 X+1  X  0  1  1
 0  0  1  1  1  0  1  0  1  1  0  X  1  1  1  0  1  0  0 X+1  1  1  1  0  X  1  X  0  1  1 X+1  1  1  0  0  1  0  1  X
 0  0  0  X  0  0  0  0  0  0  0  X  0  X  0  X  0  X  0  0  0  0  0  X  X  X  X  0  0  0  0  X  X  X  X  X  0  X  X
 0  0  0  0  X  0  0  0  0  0  0  X  X  0  X  X  0  0  0  0  X  X  X  0  0  0  0  0  X  0  X  X  0  X  0  0  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  X  0  X  0  0  X  0  X  0  X  0  0  X  0  0  X  X  0  0  X  X  0  X  0  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  X  X  0  X  0  X  X  X  0  X  X  X  X  0  X  0  0  X  0  X  X
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  0  X  0  0  X  X  0  0  X  X  X  X  X  X  X  X  0  0  X  X  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  0  X  X  X  X  X  X  0  0  0  X  0  X  X  0  X  X  0  0  X  X  0  0  0  X  X
 0  0  0  0  0  0  0  0  0  X  0  X  0  X  0  X  X  0  X  X  X  X  0  0  X  X  X  X  0  0  0  X  0  0  X  0  0  0  X
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  X  0  X  X  0  X  X  0  0  0  X  X  X  X  0  X  X  X  X  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+229x^28+292x^30+1040x^32+1274x^34+2445x^36+2722x^38+3223x^40+2196x^42+1730x^44+600x^46+467x^48+82x^50+74x^52+2x^54+5x^56+1x^60+1x^68

The gray image is a linear code over GF(2) with n=78, k=14 and d=28.
This code was found by Heurico 1.16 in 16.7 seconds.