The generator matrix

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

generates a code of length 6 over Z3[X]/(X^3) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+22x^9+378x^10+1008x^12+756x^13+18x^15+4x^18

The gray image is a linear code over GF(3) with n=54, k=7 and d=27.
This code was found by Heurico 1.16 in 0.000999 seconds.