The generator matrix

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

generates a code of length 40 over Z3[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+664x^72+1188x^75+1326x^78+1332x^81+954x^84+762x^87+280x^90+54x^93

The gray image is a linear code over GF(3) with n=120, k=8 and d=72.
This code was found by Heurico 1.16 in 0.454 seconds.