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

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+282x^77+256x^78+840x^80+582x^81+324x^82+1428x^83+2790x^84+1296x^85+2094x^86+4802x^87+1296x^88+1752x^89+696x^90+558x^92+230x^93+270x^95+68x^96+54x^98+42x^99+12x^101+2x^102+4x^105+2x^108+2x^111

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 81.3 seconds.