The generator matrix

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

generates a code of length 6 over Z3[X]/(X^3) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+26x^9+108x^10+348x^12+216x^13+30x^15

The gray image is a linear code over GF(3) with n=54, k=6 and d=27.
This code was found by Heurico 1.16 in 0.00028 seconds.