The generator matrix

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

generates a code of length 37 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+220x^28+454x^30+901x^32+1126x^34+1397x^36+1336x^38+1290x^40+776x^42+490x^44+146x^46+47x^48+2x^50+5x^52+1x^64

The gray image is a linear code over GF(2) with n=74, k=13 and d=28.
This code was found by Heurico 1.16 in 4.3 seconds.