The generator matrix

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

generates a code of length 43 over Z3[X]/(X^3) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+300x^79+438x^80+846x^81+858x^82+2148x^83+1558x^84+1956x^85+3084x^86+1972x^87+2214x^88+2256x^89+1080x^90+366x^91+264x^92+86x^93+96x^94+48x^95+30x^96+42x^97+24x^98+12x^99+2x^105+2x^108

The gray image is a linear code over GF(3) with n=387, k=9 and d=237.
This code was found by Heurico 1.16 in 25.6 seconds.