The generator matrix

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

generates a code of length 38 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+232x^28+702x^30+1306x^32+1830x^34+2599x^36+2832x^38+2852x^40+1980x^42+1246x^44+526x^46+191x^48+62x^50+19x^52+4x^54+2x^56

The gray image is a linear code over GF(2) with n=76, k=14 and d=28.
This code was found by Heurico 1.16 in 31.9 seconds.