The generator matrix

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

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+180x^8+256x^9+432x^10+1440x^11+2268x^12+2592x^13+8208x^14+8400x^15+6642x^16+13536x^17+8176x^18+3456x^19+2880x^20+576x^21+6x^24

The gray image is a linear code over GF(3) with n=24, k=10 and d=8.
This code was found by Heurico 1.16 in 1.58 seconds.