The generator matrix
1 0 1 1 1 0 1 1 0 1 1 X 1 1 1 0 1 0 1 0 1 1 1
0 1 1 0 1 1 0 1 1 X X+1 1 0 0 X+1 1 X+1 1 X+1 1 0 0 0
0 0 X 0 0 0 0 0 0 0 X 0 X X X 0 X X X X X 0 0
0 0 0 X 0 0 0 0 0 X 0 0 X 0 X 0 0 X X X X X X
0 0 0 0 X 0 0 0 X 0 X X 0 X 0 0 X 0 X 0 X X X
0 0 0 0 0 X 0 0 X 0 0 0 X X 0 X X X X X X X X
0 0 0 0 0 0 X 0 X X 0 X X X 0 0 0 0 X X 0 X X
0 0 0 0 0 0 0 X X 0 X X X 0 X X 0 0 X X X X X
generates a code of length 23 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.
Homogenous weight enumerator: w(x)=1x^0+47x^16+56x^18+208x^20+184x^22+262x^24+136x^26+100x^28+8x^30+18x^32+4x^36
The gray image is a linear code over GF(2) with n=46, k=10 and d=16.
This code was found by Heurico 1.16 in 0.0339 seconds.