The generator matrix

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

generates a code of length 8 over Z3[X]/(X^3) 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+14598x^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=72, k=9 and d=30.
This code was found by Heurico 1.16 in 0.0734 seconds.