The generator matrix

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

generates a code of length 43 over Z3[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+212x^78+462x^79+1698x^80+2442x^81+3678x^82+5022x^83+4644x^84+6120x^85+7656x^86+7552x^87+7362x^88+5706x^89+2680x^90+1758x^91+1224x^92+660x^93+36x^94+48x^95+24x^96+24x^97+30x^98+8x^99+2x^108

The gray image is a linear code over GF(3) with n=387, k=10 and d=234.
This code was found by Heurico 1.16 in 4.59 seconds.