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.