The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  X  1  1  0  1  1  0  1  1  0  1  0  X  1  0  1  0  1  1  1  0  1  0  1  0  1  1  X
 0  1  1  0  1  1  0  1  1  0  1  1  0 X+1  1 X+1  0  1  0 X+1  1  0  1  1 X+1  1  0  1  X  0 X+1  1 X+1  1  1  1  1  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  X  X  X  X  X  X  0  X  X  X
 0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  X  X  0  0  0  X  X  0  0  0  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  0  0  X  X  X  0  X  X  X  X  0  X  0  0  X  X  0  X  X
 0  0  0  0  0  X  0  0  0  0  0  X  0  X  0  X  X  X  0  X  0  X  X  X  X  X  X  X  0  X  X  0  0  0  X  X  X  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  0  0  X  X  X  0  X  X  0  X  0  X  0  X  0  X  0  0  0  X  0  0  X  0
 0  0  0  0  0  0  0  X  0  0  0  0  X  0  X  0  0  X  0  0  X  0  0  X  X  X  0  X  X  0  0  X  0  X  0  X  X  X  X
 0  0  0  0  0  0  0  0  X  0  0  X  X  0  0  X  0  X  X  X  X  0  X  0  0  0  X  0  X  0  X  X  X  0  X  X  X  0  X
 0  0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  X  X  0  0  X  X  0  X  0  X  X  0  0  X  0  X  X  0  0  0  X  X  X
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  0  X  X  X  0  0  0  X  X  X  X  0  X  0  0  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+162x^28+66x^30+537x^32+606x^34+1402x^36+1172x^38+1740x^40+956x^42+938x^44+266x^46+278x^48+6x^50+54x^52+4x^56+4x^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 5.33 seconds.