The generator matrix

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

generates a code of length 5 over Z3[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+258x^6+36x^7+1998x^8+944x^9+11430x^10+3996x^11+978x^12+36x^13+6x^15

The gray image is a linear code over GF(3) with n=45, k=9 and d=18.
This code was found by Heurico 1.16 in 0.0131 seconds.