The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  0  0  1  X  1  0  X  X  1  1  X  0  0  1  1  1  1  1  X  1  1  1  1  0  X  0  1  X
 0  1  0  0  0  0  0  0  0  1 X+1  1  1  X  1 X+1  1  X  1  0  1  0  1  1  1 X+1 X+1  0  1  1  1  0  X  X  X  X  1  X  1
 0  0  1  0  0  0  1  1  1  1  1  0  1  X  0  0  1  1  1  1  0  0 X+1  0  X  1  0  0  0  1 X+1 X+1  1  X  X  1 X+1  1  0
 0  0  0  1  0  1  1  0  1  0  0 X+1  X X+1  0 X+1  1 X+1 X+1  1  0  1  0 X+1  1 X+1  X  X  0  X  1  0  X X+1  1  1  1  1  1
 0  0  0  0  1  1  0  1  1  0  1  1 X+1  X  1  1  0  0  1 X+1  1  1  0  X  X  0  0 X+1  X  1 X+1  1  0  X X+1 X+1  X X+1  0
 0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  0  X  X  X  X  X  X  X  X  0  X  X  X  X  X  X  X  X  X  0  X  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  X  X  0  0  X  X  0  0  X  0  X  X  X  0  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  0  0  X  X  X  0  X  0  X  X  X  0  0  0  0  X  0  X  X  0  X  X  0
 0  0  0  0  0  0  0  0  X  0  X  0  0  X  X  0  X  X  X  0  0  X  0  X  X  X  X  X  X  0  X  X  0  X  0  0  X  X  X
 0  0  0  0  0  0  0  0  0  X  X  X  X  0  X  X  X  0  X  0  X  0  X  X  0  0  0  X  0  0  0  X  X  X  0  X  X  X  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+287x^28+884x^30+1927x^32+2876x^34+4666x^36+5448x^38+5915x^40+4864x^42+3267x^44+1548x^46+738x^48+228x^50+84x^52+24x^54+11x^56

The gray image is a linear code over GF(2) with n=78, k=15 and d=28.
This code was found by Heurico 1.16 in 61.9 seconds.