The generator matrix

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

generates a code of length 8 over Z3[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+20x^12+32x^15+162x^16+8x^18+16x^21+4x^24

The gray image is a linear code over GF(3) with n=24, k=5 and d=12.
This code was found by Heurico 1.16 in 0.000281 seconds.