The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  X  1  1  0  1  0  1  1  1  0  X  1  1  1  1  1  0  1  1  0  1  1  0  1  0  1  1
 0  1  1  0  1  1  0  1  1  0 X+1  1  X X+1  1 X+1  1  0  0 X+1  1  1 X+1 X+1 X+1  0 X+1  1  0 X+1  1  0  1  1  X  1  X X+1
 0  0  X  0  0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  0  0  0  0  0  X  X  X  X  X  X  0  X  X  X  X  0  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  0  X  X  X  0  X  X  0  0  0  0  X  X  X  X  0  0  0  0  0  X  X  0
 0  0  0  0  X  0  0  0  0  0  X  0  0  0  X  X  X  0  X  0  X  X  X  0  0  X  0  X  X  0  0  0  X  X  0  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  X  X  X  X  X  0  X  0  X  X  0  0  0  X  X  0  0  X  X  0  0  0  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  0  X  X  X  X  0  0  X  X  X  0
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  X  0  X  X  0  X  X  X  0  X  0  0  0  0  0  X  X  0  0  0  X  X  X  X
 0  0  0  0  0  0  0  0  X  0  0  X  0  X  X  0  0  X  X  X  0  X  X  0  X  0  X  0  0  0  X  X  0  X  X  0  X  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  X  0  X  X  X  0  0  X  0  0  X  X  X  0  X  0  X  0  0  0  0  X  X  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+103x^28+60x^30+385x^32+368x^34+791x^36+680x^38+811x^40+368x^42+365x^44+60x^46+81x^48+21x^52+1x^56+1x^64

The gray image is a linear code over GF(2) with n=76, k=12 and d=28.
This code was found by Heurico 1.16 in 1.28 seconds.