The generator matrix

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

generates a code of length 43 over Z3[X]/(X^2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+366x^80+234x^81+258x^83+158x^84+324x^86+108x^87+198x^89+106x^90+186x^92+88x^93+90x^95+18x^96+30x^98+10x^99+6x^101+4x^102+2x^111

The gray image is a linear code over GF(3) with n=129, k=7 and d=80.
This code was found by Heurico 1.16 in 40.2 seconds.