The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  X  1  1  X  X  1  1  1  1  0  0  0  1  1  0  1  X  1  0  1  1  X  1  1  0
 0  1  0  1  0  1  1  0  0  1 X+1  1  X  1  0  1  1  1  X  X X+1 X+1  1  0  0  X  0  1 X+1  1  0  0  1  X  1  1 X+1  1
 0  0  1  1  1  0  1  0  1  1  0  X  1  1  X  1  1  1  1 X+1  1  0  0  1  1  1  0  X  0  0  0  1  X  0  X  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  0  X  X  X  0  X  0  X  X  X  X  X
 0  0  0  0  X  0  0  0  0  0  X  X  X  0  0  X  0  0  0  X  X  X  X  X  0  0  0  0  X  X  0  0  0  0  0  0  X  X
 0  0  0  0  0  X  0  0  0  0  X  0  0  X  X  X  0  X  0  X  X  0  X  0  X  0  0  0  X  0  0  X  0  X  X  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  X  0  0  0  0  0  X  X  X  0  X  X  X  X  0  X  0  0  X  0  X
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  X  X  0  X  0  X  X  0  X  0  X  X  X  X  X  0  0  X  X  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  0  0  X  X  X  0  0  X  X  X  X  X  0  0  0  0  X  0  0  X  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  0  0  0  X  X  X  0  X  X  0  0  X  X  0  0  X  0  0  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+150x^28+256x^30+681x^32+912x^34+1414x^36+1320x^38+1492x^40+904x^42+714x^44+184x^46+126x^48+8x^50+26x^52+4x^56

The gray image is a linear code over GF(2) with n=76, k=13 and d=28.
This code was found by Heurico 1.16 in 4.37 seconds.