The generator matrix

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

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+114x^6+646x^9+7770x^12+34992x^14+14178x^15+1306x^18+42x^21

The gray image is a linear code over GF(3) with n=63, k=10 and d=18.
This code was found by Heurico 1.16 in 0.16 seconds.