The generator matrix

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

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+24x^6+12x^7+198x^8+80x^9+1380x^10+396x^11+78x^12+12x^13+6x^15

The gray image is a linear code over GF(3) with n=45, k=7 and d=18.
This code was found by Heurico 1.16 in 0.000395 seconds.