The generator matrix

 1  0  0  0  0  0  1  1  1  0  1  1  X  1  0  1  1  1  X  0  1  1  1  X  1  X  X  X  1  1  X  0  1  0  1  1  1  X
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  X  1  1  1  1  X  1  X X+1  1  0  1  X  X X+1 X+1  1  1  X  1  0  0 X+1  1
 0  0  1  0  0  0  0  0  0  0  1  1  1 X+1  1 X+1  X  1  1  0  X X+1  X  0  1  0  X  1  X  X  0 X+1 X+1  1 X+1  1  0  1
 0  0  0  1  0  0  0  1  1  1  X  1 X+1 X+1 X+1  X  0  X X+1  1  X  0  1 X+1  X  1  X X+1  X  1 X+1 X+1  1  X X+1 X+1  X  X
 0  0  0  0  1  0  1  1  0 X+1  X  0  X X+1  1 X+1  X  X  0  1  1  1  X X+1 X+1 X+1  1  X  0  X  1 X+1  0  0  1  1  X  0
 0  0  0  0  0  1  1  0 X+1 X+1  1  X X+1 X+1  X  1 X+1  0  X  0  1  1  1 X+1  0  0 X+1  0  1  X  X  0  0  0  0  X  X X+1
 0  0  0  0  0  0  X  0  X  X  X  0  X  X  0  X  X  0  0  X  0  0  0  0  X  0  X  X  0  0  X  0  X  X  X  X  0  X
 0  0  0  0  0  0  0  X  0  X  0  X  X  0  0  0  0  X  0  X  X  X  X  0  X  X  0  0  0  0  0  X  X  0  0  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+206x^28+744x^30+1283x^32+1894x^34+2557x^36+2782x^38+2828x^40+2080x^42+1194x^44+520x^46+232x^48+42x^50+17x^52+2x^54+2x^60

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 33 seconds.