The generator matrix

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

generates a code of length 10 over Z3[X]/(X^3) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+44x^9+136x^12+276x^15+500x^18+17496x^20+580x^21+426x^24+184x^27+40x^30

The gray image is a linear code over GF(3) with n=90, k=9 and d=27.
This code was found by Heurico 1.16 in 0.0867 seconds.