The generator matrix

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

generates a code of length 7 over Z3[X]/(X^3) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+12x^13+54x^14+6x^15+6x^16+2x^18

The gray image is a linear code over GF(3) with n=63, k=4 and d=39.
This code was found by Heurico 1.16 in 8.8e-005 seconds.