The generator matrix

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

generates a code of length 23 over Z2[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+173x^18+410x^19+796x^20+892x^21+1167x^22+1268x^23+1311x^24+874x^25+704x^26+362x^27+194x^28+24x^29+3x^30+8x^31+2x^32+2x^33+1x^34

The gray image is a linear code over GF(2) with n=92, k=13 and d=36.
This code was found by Heurico 1.11 in 0.266 seconds.