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.