The generator matrix
1 0 0 0 0 1 1 1 1 X^2 1 X 1 X 0 X 1 1 1 0 X 1 1
0 1 0 0 0 0 X 1 X^2+1 1 1 X X 1 1 1 X^2+X+1 X^2+X X 1 1 X^2+X+1 X^2+X
0 0 1 0 0 0 X+1 X X^2+1 X^2+X+1 0 1 X^2+X+1 X^2 X^2 X+1 X^2+1 X X+1 X+1 X^2+1 X^2+1 X^2
0 0 0 1 0 1 1 X+1 X^2 1 0 X^2+1 X X^2+1 X^2+X+1 X^2+X X+1 1 0 X 0 X^2+1 X+1
0 0 0 0 1 1 X^2 0 X X 1 X^2+1 1 0 X^2+1 X^2+X+1 X+1 X^2+X X^2+X 0 X+1 X^2+X X^2+1
0 0 0 0 0 X 0 0 0 0 X^2 0 X^2 X^2 X X X^2+X X X^2+X X^2+X X^2 X^2 X
generates a code of length 23 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.
Homogenous weight enumerator: w(x)=1x^0+385x^16+992x^17+2912x^18+4896x^19+10327x^20+14376x^21+20888x^22+20968x^23+21652x^24+14256x^25+10356x^26+5040x^27+2728x^28+840x^29+336x^30+72x^31+42x^32+4x^34+1x^36
The gray image is a linear code over GF(2) with n=92, k=17 and d=32.
This code was found by Heurico 1.13 in 45.8 seconds.