The generator matrix

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

generates a code of length 6 over Z3[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+42x^6+18x^7+162x^8+238x^9+2106x^10+648x^11+11304x^12+4158x^13+648x^14+318x^15+36x^16+4x^18

The gray image is a linear code over GF(3) with n=54, k=9 and d=18.
This code was found by Heurico 1.16 in 0.0179 seconds.