The generator matrix

 1  0  1  1  1
 0  1  1  2  0
 0  0 2X  0  X
 0  0  0  X  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+38x^6+162x^8+92x^9+324x^11+102x^12+10x^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 0.000187 seconds.