The generator matrix

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

generates a code of length 43 over Z3[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+708x^78+1266x^81+1194x^84+1320x^87+988x^90+624x^93+384x^96+76x^99

The gray image is a linear code over GF(3) with n=129, k=8 and d=78.
This code was found by Heurico 1.16 in 27.6 seconds.