The generator matrix
1 0 1 1 1 0 1 1 0 1 1 X 1 1 0 1 1 0 1 1 0 0 1 X 1 1 0 1 0 1 X 1 0 1 1 1 1
0 1 1 0 1 1 0 1 1 X X+1 1 0 X+1 1 0 X+1 1 0 X+1 1 1 X 1 0 X+1 1 0 1 0 1 X+1 1 X+1 1 0 0
0 0 X 0 0 0 0 0 0 0 X 0 0 0 X 0 0 X X 0 0 0 X X X X X X 0 X 0 X X 0 0 0 0
0 0 0 X 0 0 0 0 0 X 0 0 0 0 X X X X X 0 X 0 0 0 X X 0 X X X X 0 0 X X 0 0
0 0 0 0 X 0 0 0 0 0 X 0 X 0 0 X X X 0 X X 0 X 0 X 0 0 0 0 X 0 0 X X X 0 0
0 0 0 0 0 X 0 0 0 0 0 X X 0 0 X 0 0 X X X X 0 0 X 0 X X X X 0 X 0 0 0 X X
0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X 0 X X 0 0 X 0 X 0 X X 0 0 X X X X 0 X X
0 0 0 0 0 0 0 X 0 0 X 0 X X X X 0 0 0 X 0 X X 0 X X X X 0 0 0 0 0 X 0 0 0
0 0 0 0 0 0 0 0 X 0 0 X X X X 0 X 0 0 X X 0 X X X 0 X 0 X 0 0 0 0 0 X 0 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+74x^28+60x^30+261x^32+240x^34+431x^36+312x^38+341x^40+144x^42+128x^44+12x^46+36x^48+7x^52+1x^56
The gray image is a linear code over GF(2) with n=74, k=11 and d=28.
This code was found by Heurico 1.16 in 0.307 seconds.