The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+12x^3+18x^4+60x^6+144x^7+160x^9+1404x^10+14820x^12+2520x^13+192x^15+288x^16+64x^18

The gray image is a linear code over GF(3) with n=54, k=9 and d=9.
This code was found by Heurico 1.16 in 0.0222 seconds.