The generator matrix

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

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+666x^72+1152x^75+1410x^78+1286x^81+918x^84+786x^87+318x^90+18x^93+6x^99

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 71.3 seconds.