The generator matrix

 1  0  1  1  1  1  1  1
 0  1  1  2  0  0  0  0
 0  0 2X  0  0  0  X  0
 0  0  0  X  0  0  X  0
 0  0  0  0  X  0  X  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+48x^6+160x^9+372x^12+1458x^14+540x^15+2916x^17+604x^18+420x^21+42x^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 0.00569 seconds.