The generator matrix

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

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+6x^6+8x^9+54x^10+6x^12+6x^15

The gray image is a linear code over GF(3) with n=15, k=4 and d=6.
This code was found by Heurico 1.16 in 5.79e-005 seconds.