The generator matrix

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

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+58x^12+216x^14+48x^15+216x^17+128x^18+54x^20+8x^21

The gray image is a linear code over GF(3) with n=24, k=6 and d=12.
This code was found by Heurico 1.16 in 0.00085 seconds.