The generator matrix

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

generates a code of length 7 over Z3[X]/(X^3) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+52x^9+162x^10+720x^12+648x^13+2916x^14+1314x^15+648x^16+100x^18

The gray image is a linear code over GF(3) with n=63, k=8 and d=27.
This code was found by Heurico 1.16 in 0.761 seconds.