The generator matrix

 1  0  0  0  0  0  1  1  1  X  1  1  X  1  X  1  X  0  X  X  1  1  1  1  X  1  X  1  X  0  X  1  1  1  X  1  X
 0  1  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0 X+1  1  1  1 X+1  1 X+1  1  1  1  X  1  0  1  1  0
 0  0  1  0  0  0  0  0  0  0  1  1  1 X+1  1 X+1  1  0  X  0  X  X X+1 X+1  1  0  1  X  0 X+1  X X+1  0  X  0  1  1
 0  0  0  1  0  0  0  1  1  1  1 X+1  0  0 X+1  X  1  1  X  0  1  0 X+1  X X+1  1  0 X+1  0  X  X  0  X  X  X  X  X
 0  0  0  0  1  0  1  1  X X+1  0 X+1  1  1 X+1  0  0 X+1  X  1  X  0  X  X X+1  0  1 X+1  X  X  1  X X+1  1 X+1 X+1  X
 0  0  0  0  0  1  1  X X+1  1  0  1  1  0  0  1  1  1  1  X X+1  X X+1  1  0  1 X+1  X X+1  X  0  0 X+1  X  X  0  1
 0  0  0  0  0  0  X  0  X  0  X  0  0  X  0  0  0  X  X  X  0  X  0  X  X  0  X  0  0  X  X  0  X  X  0  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+171x^28+532x^30+929x^32+1074x^34+1381x^36+1340x^38+1230x^40+872x^42+469x^44+144x^46+39x^48+6x^50+3x^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 4.42 seconds.