The generator matrix
1 0 0 0 1 1 1 0 1 1 1 1 X 0 1 1 X 1 1 X 0 1 X 0 1 1 X 0 1 X 1 1 X 1 1 0 X
0 1 0 0 0 1 1 1 X 0 X+1 1 1 X X 0 1 X+1 0 1 1 0 1 X X 1 0 0 X 1 0 1 1 1 X 1 0
0 0 1 0 1 1 0 1 0 X+1 X X+1 X 1 0 X X+1 0 X+1 X+1 X X 0 1 1 0 1 1 X 1 X+1 0 X+1 X+1 0 0 0
0 0 0 1 1 0 1 X+1 1 X X X+1 X+1 1 X X+1 X 0 0 X 1 0 0 X 1 0 X+1 0 0 1 X X+1 X+1 X 1 0 X
0 0 0 0 X 0 0 X 0 X 0 0 0 X X X X 0 0 0 0 X 0 0 X X X 0 X 0 0 0 X X 0 X 0
0 0 0 0 0 X 0 0 0 0 0 0 X X X X X X X X X X X X X X 0 0 0 X X X X X X X X
0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 X X X X X X X 0 X X X X 0 0 0 X X X 0
generates a code of length 37 over Z2[X]/(X^2) who´s minimum homogenous weight is 30.
Homogenous weight enumerator: w(x)=1x^0+143x^30+282x^32+308x^34+316x^36+326x^38+286x^40+192x^42+124x^44+51x^46+15x^48+4x^50
The gray image is a linear code over GF(2) with n=74, k=11 and d=30.
This code was found by Heurico 1.16 in 0.277 seconds.