The generator matrix

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

generates a code of length 7 over Z3[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+38x^6+102x^9+1130x^12+2916x^14+2158x^15+194x^18+22x^21

The gray image is a linear code over GF(3) with n=63, k=8 and d=18.
This code was found by Heurico 1.16 in 0.00437 seconds.