The generator matrix

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

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+192x^28+508x^30+893x^32+1064x^34+1496x^36+1292x^38+1230x^40+836x^42+484x^44+136x^46+50x^48+4x^50+4x^52+2x^56

The gray image is a linear code over GF(2) with n=74, k=13 and d=28.
This code was found by Heurico 1.10 in 1.44 seconds.