The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+84x^6+54x^7+162x^8+382x^9+972x^10+648x^11+1170x^12+1782x^13+648x^14+546x^15+108x^16+4x^18

The gray image is a linear code over GF(3) with n=18, k=8 and d=6.
This code was found by Heurico 1.16 in 0.016 seconds.