The generator matrix

 1  0  1  1  1  1  1  1
 0  1  1  0  2 2X+1  2  X
 0  0 2X  X 2X  X  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+14x^12+18x^13+18x^14+60x^15+18x^16+36x^17+56x^18+18x^19+4x^21

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 0.000225 seconds.