The generator matrix

 1  0  0  0  1  1  1  X  1  1  1 X^2+X  0 X^2+X X^2+X  1  1 X^2 X^2  0  1  0  1
 0  1  0  0 X^2  1 X^2+1  1 X^2+X  X X+1  0  1  1  X X^2+1 X^2+X+1  1  X  X  1  1  0
 0  0  1  0 X^2+1  1 X^2 X^2+X+1  1  0 X^2+X+1  1  X X^2+X  1 X+1 X^2  1  1  1  X  X  0
 0  0  0  1  1 X^2 X^2+X+1 X^2+X+1  X  1 X+1 X^2+X+1 X^2+X+1 X^2+1 X^2+X+1 X^2+1  0 X^2+X X+1 X^2+1 X+1  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+58x^18+276x^19+378x^20+530x^21+558x^22+584x^23+475x^24+528x^25+374x^26+224x^27+64x^28+30x^29+10x^30+4x^31+2x^32

The gray image is a linear code over GF(2) with n=92, k=12 and d=36.
This code was found by Heurico 1.16 in 0.158 seconds.