The generator matrix
1 1 1 1 1
0 X^2 0 X^2 0
0 0 X^2 2X^2 0
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+6x^6+8x^9+216x^10+6x^12+6x^15
The gray image is a linear code over GF(3) with n=45, k=5 and d=18.
This code was found by Heurico 1.16 in 5.7e-005 seconds.