The generator matrix

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

generates a code of length 10 over Z3[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+158x^18+48x^19+180x^20+314x^21+24x^22+2x^24+2x^27

The gray image is a linear code over GF(3) with n=90, k=6 and d=54.
This code was found by Heurico 1.16 in 0.000379 seconds.