The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  1  0  1  1  0  1  X  1  1  1  1  1  1  1  X  1  1  1  1  1  X  X  X  1  1
 0  1  0  1  0  1  1  0  0  1 X+1  1  1  X  0  X  1  1  1  1 X+1  0  X  X X+1  X X+1  1  1  X X+1 X+1  0  1  X  X  0  0
 0  0  1  1  1  0  1  0  1 X+1  X  X  1  0  1  1  1  0  1  1 X+1  X X+1  X  X  1  0  0 X+1  1 X+1  1  X  1  1  1  0  0
 0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  0  X  X  X  0  0  0  X  X  0  X  X  X  0  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  0  X  0  X  X  0  X  0  X  X  X  X  0  0  0  X  X  0  X  X  X  0  0
 0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  X  X  X  X  0  X  0  X  0  X  X  X  0  X  0  X  0  0  X  0  0  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  0  X  0  X  X  X  X  0  X  0  0  X  0  0  0  X  X  0  X  X
 0  0  0  0  0  0  0  X  0  X  X  0  0  0  X  0  X  X  X  0  0  X  X  X  0  X  0  X  X  X  X  0  0  X  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  0  0  X  X  0  X  0  X  0  X  X  0  X  X  0  X  0  0  0  X  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+34x^28+160x^30+338x^32+523x^34+657x^36+702x^38+659x^40+498x^42+304x^44+152x^46+49x^48+11x^50+5x^52+2x^54+1x^56

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 1.1 seconds.