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  0  X  0  X 2X 2X 2X  0  0  X  X  0  X  X  X 2X 2X  0  X 2X  0 2X
 0  0  X 2X 2X  X  0  X 2X  0  X 2X  X 2X  0 2X  X  0  X 2X  0 2X  X  0

generates a code of length 24 over Z3[X]/(X^2) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+48x^47+12x^48+12x^51+2x^54+6x^56

The gray image is a linear code over GF(3) with n=72, k=4 and d=47.
This code was found by Heurico 1.16 in 0.00215 seconds.