The generator matrix

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

generates a code of length 8 over Z3[X]/(X^3) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+14x^15+54x^16+10x^18+2x^21

The gray image is a linear code over GF(3) with n=72, k=4 and d=45.
This code was found by Heurico 1.16 in 0.000122 seconds.