The generator matrix

 1  0  0  0  1  1  1  1
 0  1  0  0  1  0 2X+1  0
 0  0  1  0  2  1 2X+1  0
 0  0  0  1  2  2 2X+1  0
 0  0  0  0 2X  0  X  0
 0  0  0  0  0 2X 2X  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+540x^8+268x^9+324x^10+2376x^11+3054x^12+1944x^13+7128x^14+6732x^15+8262x^16+11448x^17+8812x^18+2592x^19+4752x^20+708x^21+42x^24

The gray image is a linear code over GF(3) with n=24, k=10 and d=6.
This code was found by Heurico 1.16 in 0.368 seconds.