The generator matrix

 1  0  1  1  1  1  1
 0  1  1  2 2X^2+2X+1  0  2
 0  0 2X  0 2X^2 2X X^2+2X
 0  0  0 X^2 2X^2 2X^2 X^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+324x^10+2664x^12+1296x^13+8748x^14+5202x^15+1296x^16+100x^18

The gray image is a linear code over GF(3) with n=63, k=9 and d=27.
This code was found by Heurico 1.16 in 0.0474 seconds.