The generator matrix

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

generates a code of length 24 over Z3[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+66x^45+126x^48+18x^51+32x^54

The gray image is a linear code over GF(3) with n=72, k=5 and d=45.
This code was found by Heurico 1.16 in 0.00199 seconds.