The generator matrix

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

generates a code of length 7 over Z3[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+2x^12+24x^13+198x^14+4x^15+12x^16+2x^21

The gray image is a linear code over GF(3) with n=63, k=5 and d=36.
This code was found by Heurico 1.16 in 0.000124 seconds.