The generator matrix
1 1 1 1 1 1 1 1
0 X 0 0 2X 2X^2+X X 2X
0 0 X 2X 0 2X^2+2X X 2X
0 0 0 X^2 0 2X^2 0 X^2
0 0 0 0 X^2 X^2 0 X^2
generates a code of length 8 over Z3[X]/(X^3) who´s minimum homogenous weight is 9.
Homogenous weight enumerator: w(x)=1x^0+22x^9+144x^10+258x^12+864x^13+924x^15+15336x^16+940x^18+1152x^19+30x^21+12x^24
The gray image is a linear code over GF(3) with n=72, k=9 and d=27.
This code was found by Heurico 1.16 in 0.0722 seconds.