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

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+312x^72+486x^78+1190x^81+160x^90+36x^99+2x^117

The gray image is a linear code over GF(3) with n=120, k=7 and d=72.
This code was found by Heurico 1.16 in 46.1 seconds.