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.