The generator matrix

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

generates a code of length 23 over Z2[X]/(X^3) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+110x^17+348x^18+792x^19+1338x^20+1768x^21+2314x^22+2778x^23+2619x^24+1958x^25+1239x^26+654x^27+296x^28+116x^29+32x^30+14x^31+2x^32+3x^34+2x^35

The gray image is a linear code over GF(2) with n=92, k=14 and d=34.
This code was found by Heurico 1.13 in 0.922 seconds.