The generator matrix

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

generates a code of length 5 over Z3[X]/(X^2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+18x^8+14x^9+36x^11+12x^12

The gray image is a linear code over GF(3) with n=15, k=4 and d=8.
This code was found by Heurico 1.16 in 9.42e-005 seconds.