The generator matrix

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

generates a code of length 8 over Z3[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+56x^6+112x^9+420x^12+560x^15+4374x^16+616x^18+336x^21+86x^24

The gray image is a linear code over GF(3) with n=24, k=8 and d=6.
This code was found by Heurico 1.16 in 0.00942 seconds.