The generator matrix

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

generates a code of length 40 over Z3[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+702x^72+54x^74+1152x^75+486x^76+324x^77+2724x^78+1944x^79+3564x^80+4212x^81+1944x^82+432x^83+1158x^84+678x^87+240x^90+66x^93+2x^108

The gray image is a linear code over GF(3) with n=360, k=9 and d=216.
This code was found by Heurico 1.16 in 28.2 seconds.