The generator matrix

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

generates a code of length 40 over Z3[X]/(X^2) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+36x^79+14x^81+18x^82+6x^84+6x^87

The gray image is a linear code over GF(3) with n=120, k=4 and d=79.
This code was found by Heurico 1.16 in 0.0055 seconds.