The generator matrix

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

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+174x^18+460x^19+744x^20+808x^21+1200x^22+1320x^23+1399x^24+832x^25+651x^26+364x^27+158x^28+56x^29+22x^30+2x^32+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 1.16 in 0.636 seconds.