The generator matrix

 1  0  0  0  1  1  1  1 2X  1  1  1  1  0  1  1  1 2X 2X  0  1  1  1 2X
 0  1  0  0  0  1 2X  2  1 2X+1 X+2 2X  2  1 2X  1  0  1  1  1 2X+2 2X+1 2X  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  2 2X+2  X X+2  1  1
 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  1  0 X+2  2  X X+2
 0  0  0  0 2X 2X  X  0 2X 2X 2X 2X  X  X  0  X  X  X 2X 2X  X  0  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+624x^39+2212x^42+3924x^45+5430x^48+5010x^51+2252x^54+210x^57+12x^60+6x^63+2x^69

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 2.78 seconds.