The generator matrix

 1  0  1  1  1
 0  1  1  0  X
 0  0 2X  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+4x^6+18x^7+36x^8+8x^9+72x^10+72x^11+12x^12+18x^13+2x^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 0.000104 seconds.