The generator matrix

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

generates a code of length 24 over Z3[X]/(X^3) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+108x^47+72x^48+54x^50+8x^54

The gray image is a linear code over GF(3) with n=216, k=5 and d=141.
This code was found by Heurico 1.16 in 0.0024 seconds.