The generator matrix

 1  1  1  1  1  1
 0  X  0 2X^2+X  0  X
 0  0  X X^2+2X 2X  X
 0  0  0 X^2  0 2X^2
 0  0  0  0 X^2 X^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+66x^6+486x^8+256x^9+1944x^11+14616x^12+1944x^14+348x^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 0.0314 seconds.