The generator matrix

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

generates a code of length 40 over Z3[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+36x^78+162x^80+26x^81+12x^84+6x^93

The gray image is a linear code over GF(3) with n=120, k=5 and d=78.
This code was found by Heurico 1.16 in 0.00879 seconds.