The generator matrix

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

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+162x^18+324x^20+216x^21+18x^24+8x^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 0.000922 seconds.