The generator matrix

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

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+324x^8+364x^9+486x^10+1296x^11+1224x^12+972x^13+1296x^14+492x^15+22x^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 0.00622 seconds.