The generator matrix

 1  0  1  1  1
 0  1 2X^2+2X+1  2  0
 0  0 2X^2  0 X^2
 0  0  0 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+92x^6+648x^8+308x^9+3888x^10+1296x^11+318x^12+10x^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 0.00218 seconds.