The generator matrix

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

generates a code of length 8 over Z3[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+96x^10+240x^11+92x^12+576x^13+792x^14+320x^15+1476x^16+1584x^17+296x^18+768x^19+300x^20+16x^21+4x^24

The gray image is a linear code over GF(3) with n=24, k=8 and d=10.
This code was found by Heurico 1.16 in 0.031 seconds.