The generator matrix

 1  1  1  1  1  1
 0 X^2  0  0  0 X^2
 0  0 X^2  0  0 2X^2
 0  0  0 X^2  0 2X^2
 0  0  0  0 X^2 X^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+30x^6+40x^9+2034x^12+60x^15+22x^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 0.000741 seconds.