The generator matrix

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

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+30x^6+52x^9+324x^10+1026x^12+648x^13+96x^15+10x^18

The gray image is a linear code over GF(3) with n=54, k=7 and d=18.
This code was found by Heurico 1.16 in 0.00061 seconds.