The generator matrix

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

generates a code of length 5 over Z3[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+42x^6+36x^7+54x^8+80x^9+252x^10+108x^11+114x^12+36x^13+6x^15

The gray image is a linear code over GF(3) with n=15, k=6 and d=6.
This code was found by Heurico 1.16 in 0.000165 seconds.