The generator matrix

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

generates a code of length 8 over Z3[X]/(X^3) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+20x^9+18x^10+154x^12+108x^13+648x^14+496x^15+3132x^16+1296x^17+492x^18+144x^19+44x^21+8x^24

The gray image is a linear code over GF(3) with n=72, k=8 and d=27.
This code was found by Heurico 1.16 in 0.00732 seconds.