The generator matrix

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

generates a code of length 39 over Z2[X]/(X^2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+198x^30+572x^32+928x^34+1082x^36+1294x^38+1316x^40+1141x^42+946x^44+500x^46+175x^48+34x^50+4x^52+1x^74

The gray image is a linear code over GF(2) with n=78, k=13 and d=30.
This code was found by Heurico 1.16 in 4.68 seconds.