The generator matrix

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

generates a code of length 8 over Z3[X]/(X^2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+20x^9+46x^12+64x^15+486x^16+60x^18+44x^21+8x^24

The gray image is a linear code over GF(3) with n=24, k=6 and d=9.
This code was found by Heurico 1.16 in 0.000573 seconds.