The generator matrix

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

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+82x^6+36x^7+594x^8+320x^9+3978x^10+1188x^11+324x^12+36x^13+2x^15

The gray image is a linear code over GF(3) with n=45, k=8 and d=18.
This code was found by Heurico 1.16 in 0.00205 seconds.