The generator matrix

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

generates a code of length 8 over Z3[X]/(X^2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+22x^9+144x^10+258x^12+864x^13+924x^15+2214x^16+940x^18+1152x^19+30x^21+12x^24

The gray image is a linear code over GF(3) with n=24, k=8 and d=9.
This code was found by Heurico 1.16 in 0.0167 seconds.