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

generates a code of length 40 over Z3[X]/(X^2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+108x^77+36x^78+26x^81+12x^84+54x^86+6x^93

The gray image is a linear code over GF(3) with n=120, k=5 and d=77.
This code was found by Heurico 1.16 in 0.0671 seconds.