The generator matrix

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

generates a code of length 43 over Z3[X]/(X^2) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+138x^79+204x^80+78x^81+240x^82+246x^83+38x^84+192x^85+186x^86+52x^87+138x^88+138x^89+28x^90+132x^91+96x^92+28x^93+96x^94+84x^95+14x^96+30x^97+18x^98+4x^99+6x^100

The gray image is a linear code over GF(3) with n=129, k=7 and d=79.
This code was found by Heurico 1.13 in 0.0312 seconds.