The generator matrix

 1  1  1  1  1  1  1  1
 0  X  0  0  0  0  X  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  0

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+30x^6+52x^9+120x^12+180x^15+1458x^16+172x^18+132x^21+42x^24

The gray image is a linear code over GF(3) with n=24, k=7 and d=6.
This code was found by Heurico 1.16 in 0.00177 seconds.