The generator matrix

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

generates a code of length 43 over Z3[X]/(X^2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+126x^82+162x^83+24x^84+96x^85+72x^86+44x^87+42x^88+54x^89+2x^90+24x^91+12x^92+6x^93+12x^94+18x^95+4x^96+12x^97+12x^100+6x^101

The gray image is a linear code over GF(3) with n=129, k=6 and d=82.
This code was found by Heurico 1.16 in 0.0848 seconds.