The generator matrix

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

generates a code of length 6 over Z3[X]/(X^2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+36x^8+60x^9+54x^10+144x^11+120x^12+108x^13+144x^14+60x^15+2x^18

The gray image is a linear code over GF(3) with n=18, k=6 and d=8.
This code was found by Heurico 1.16 in 0.000415 seconds.