The generator matrix

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

generates a code of length 43 over Z3[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+240x^77+280x^78+282x^79+450x^80+712x^81+900x^82+798x^83+2126x^84+2892x^85+1506x^86+3588x^87+2802x^88+720x^89+1008x^90+216x^91+354x^92+208x^93+132x^94+234x^95+74x^96+66x^97+72x^98+14x^99+6x^102+2x^108

The gray image is a linear code over GF(3) with n=387, k=9 and d=231.
This code was found by Heurico 1.16 in 5.39 seconds.