The generator matrix

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

generates a code of length 8 over Z3[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+48x^6+160x^9+372x^12+2916x^14+540x^15+8748x^16+5832x^17+604x^18+420x^21+42x^24

The gray image is a linear code over GF(3) with n=72, k=9 and d=18.
This code was found by Heurico 1.16 in 0.0368 seconds.