The generator matrix

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

generates a code of length 6 over Z3[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+102x^6+472x^9+1944x^10+12618x^12+3888x^13+636x^15+22x^18

The gray image is a linear code over GF(3) with n=54, k=9 and d=18.
This code was found by Heurico 1.16 in 0.019 seconds.