The generator matrix

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

generates a code of length 7 over Z3[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+66x^8+156x^9+270x^10+396x^11+454x^12+1080x^13+14562x^14+894x^15+1080x^16+528x^17+188x^18+8x^21

The gray image is a linear code over GF(3) with n=63, k=9 and d=24.
This code was found by Heurico 1.16 in 0.0448 seconds.