The generator matrix

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

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+76x^6+126x^7+342x^8+538x^9+2178x^10+2736x^11+7422x^12+11628x^13+16470x^14+24484x^15+35838x^16+27468x^17+24670x^18+15318x^19+5472x^20+1830x^21+522x^22+28x^24

The gray image is a linear code over GF(3) with n=24, k=11 and d=6.
This code was found by Heurico 1.16 in 10.1 seconds.