The generator matrix

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

generates a code of length 24 over Z3[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+1146x^36+5292x^39+16434x^42+36384x^45+53010x^48+43416x^51+18242x^54+3096x^57+90x^60+36x^63

The gray image is a linear code over GF(3) with n=72, k=11 and d=36.
This code was found by Heurico 1.16 in 232 seconds.