The generator matrix

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

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+38x^18+274x^19+359x^20+496x^21+565x^22+632x^23+587x^24+532x^25+296x^26+224x^27+69x^28+12x^29+5x^30+4x^31+2x^35

The gray image is a linear code over GF(2) with n=92, k=12 and d=36.
This code was found by Heurico 1.11 in 0.062 seconds.