The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+14x^3+84x^6+280x^9+560x^12+17496x^14+672x^15+448x^18+128x^21

The gray image is a linear code over GF(3) with n=63, k=9 and d=9.
This code was found by Heurico 1.16 in 0.0316 seconds.