The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+72x^8+76x^9+108x^10+576x^11+774x^12+648x^13+2700x^14+2784x^15+2754x^16+4248x^17+2740x^18+864x^19+1152x^20+180x^21+6x^24

The gray image is a linear code over GF(3) with n=24, k=9 and d=8.
This code was found by Heurico 1.16 in 0.187 seconds.