The generator matrix

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

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+20x^6+20x^9+162x^10+30x^12+10x^15

The gray image is a linear code over GF(3) with n=15, k=5 and d=6.
This code was found by Heurico 1.16 in 0.000102 seconds.