The generator matrix

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

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+58x^28+106x^29+184x^30+264x^31+339x^32+396x^33+457x^34+562x^35+649x^36+682x^37+708x^38+730x^39+642x^40+630x^41+526x^42+406x^43+300x^44+212x^45+156x^46+86x^47+57x^48+22x^49+17x^50+1x^52+1x^64

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 4.22 seconds.