The generator matrix

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

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+48x^47+174x^48+12x^51+2x^54+6x^56

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 0.00313 seconds.