The generator matrix

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

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+274x^17+766x^18+1382x^19+2741x^20+3336x^21+5090x^22+5142x^23+5464x^24+3820x^25+2626x^26+1138x^27+618x^28+248x^29+94x^30+18x^31+7x^32+2x^33+1x^36

The gray image is a linear code over GF(2) with n=92, k=15 and d=34.
This code was found by Heurico 1.16 in 9.62 seconds.