The generator matrix

1 0 0 0 0 1 1 1 X 0 1 1 0 1 X X 1 X 0 X X 0 1
0 1 0 0 0 0 0 0 0 X 1 1 1 X+1 X 1 X 1 1 1 1 0 0
0 0 1 0 0 0 1 1 1 1 0 X X 0 X 1 X+1 1 0 X+1 X 1 0
0 0 0 1 0 1 0 X+1 1 1 X 1 X+1 X 0 X+1 X 1 X+1 0 1 1 0
0 0 0 0 1 1 X+1 X 1 0 0 0 X+1 X+1 1 1 0 X+1 1 X 1 1 0
0 0 0 0 0 X X 0 0 X X 0 X 0 0 0 0 X X 0 0 X 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+44x^16+64x^17+121x^18+146x^19+164x^20+186x^21+176x^22+214x^23+198x^24+222x^25+170x^26+142x^27+98x^28+38x^29+40x^30+10x^31+5x^32+2x^33+5x^34+2x^36

The gray image is a linear code over GF(2) with n=46, k=11 and d=16.
This code was found by Heurico 1.10 in 0.031 seconds.