The generator matrix

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

generates a code of length 43 over Z3[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+504x^80+372x^81+2148x^82+1800x^83+1326x^84+2640x^85+2634x^86+1574x^87+2634x^88+1614x^89+626x^90+1128x^91+546x^92+60x^93+30x^94+18x^95+10x^96+12x^98+6x^100

The gray image is a linear code over GF(3) with n=387, k=9 and d=240.
This code was found by Heurico 1.16 in 0.524 seconds.