The generator matrix

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

generates a code of length 43 over Z3[X]/(X^2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+300x^77+192x^78+654x^80+478x^81+876x^83+448x^84+912x^86+308x^87+636x^89+418x^90+624x^92+232x^93+300x^95+70x^96+60x^98+28x^99+12x^101+4x^102+4x^105+2x^108+2x^114

The gray image is a linear code over GF(3) with n=129, k=8 and d=77.
This code was found by Heurico 1.16 in 0.634 seconds.