The generator matrix

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

generates a code of length 23 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+32x^20+122x^21+80x^22+108x^23+43x^24+60x^25+15x^26+28x^27+20x^28+2x^29+1x^34

The gray image is a linear code over GF(2) with n=92, k=9 and d=40.
This code was found by Heurico 1.11 in 1.05e-007 seconds.