The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  0  1 X^2+X  1  1  1  1 X^2+X  1  0  1  1  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X  1 X^2+1  1  0 X+1 X^2+X X^2+1  1  0  1 X+1 X+1  0
 0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0
 0  0  0 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2  0  0
 0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0
 0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  0 X^2  0 X^2

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+21x^16+16x^17+88x^18+96x^19+431x^20+240x^21+998x^22+320x^23+1000x^24+240x^25+430x^26+96x^27+72x^28+16x^29+18x^30+10x^32+2x^34+1x^36

The gray image is a linear code over GF(2) with n=92, k=12 and d=32.
This code was found by Heurico 1.16 in 0.169 seconds.