The generator matrix

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

generates a code of length 8 over Z3[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+102x^6+484x^9+1128x^12+5832x^14+1620x^15+34992x^16+11664x^17+1900x^18+1284x^21+42x^24

The gray image is a linear code over GF(3) with n=72, k=10 and d=18.
This code was found by Heurico 1.16 in 0.161 seconds.