The generator matrix

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

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+123x^16+418x^18+620x^20+892x^22+848x^24+708x^26+362x^28+92x^30+28x^32+2x^34+2x^36

The gray image is a linear code over GF(2) with n=46, k=12 and d=16.
This code was found by Heurico 1.10 in 0.172 seconds.