The generator matrix

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

generates a code of length 8 over Z3[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+66x^6+54x^8+268x^9+324x^10+216x^11+948x^12+1296x^13+1296x^14+2196x^15+5184x^16+2376x^17+2332x^18+1944x^19+432x^20+708x^21+42x^24

The gray image is a linear code over GF(3) with n=24, k=9 and d=6.
This code was found by Heurico 1.16 in 0.0609 seconds.