The generator matrix

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

generates a code of length 8 over Z3[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+14x^12+18x^13+72x^14+60x^15+342x^16+144x^17+56x^18+18x^19+4x^21

The gray image is a linear code over GF(3) with n=72, k=6 and d=36.
This code was found by Heurico 1.16 in 0.000413 seconds.