The generator matrix

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

generates a code of length 24 over Z3[X]/(X^2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+614x^39+2220x^42+3996x^45+5256x^48+5172x^51+2180x^54+228x^57+6x^60+6x^63+4x^66

The gray image is a linear code over GF(3) with n=72, k=9 and d=39.
This code was found by Heurico 1.16 in 1.76 seconds.