The generator matrix

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

generates a code of length 8 over Z3[X]/(X^2) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+16x^3+112x^6+448x^9+1120x^12+1792x^15+13122x^16+1792x^18+1024x^21+256x^24

The gray image is a linear code over GF(3) with n=24, k=9 and d=3.
This code was found by Heurico 1.16 in 0.0668 seconds.