The generator matrix

 1  0  0  1  1  1
 0  1  0  1  0  X
 0  0  1  2  2 2X
 0  0  0 2X  X 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+22x^6+24x^7+54x^8+132x^9+306x^10+216x^11+402x^12+612x^13+216x^14+164x^15+30x^16+8x^18

The gray image is a linear code over GF(3) with n=18, k=7 and d=6.
This code was found by Heurico 1.13 in 0.00019 seconds.