The generator matrix

 1  0  1  1  1  1  1  X  1  1 2X  1 2X^2  1  1  1  1 2X^2  1  1  1  1  1  1 2X^2  1 X^2+X  1  1  1  1  1  0  1 2X^2+X  1  X  1  1  1 X^2+2X  1  1
 0  1  1  2 2X^2 2X+1  2  1 2X^2+2X+1 2X^2+X  1  2  1  X X^2+X+1 X+2 X^2+1  1 2X^2+2  X 2X^2+X+2 2X^2+1 2X 2X^2  1 2X^2+X+1  1 2X^2 2X^2+X X^2+2X+1 X^2+2 2X+1  1 2X^2+X+2  1  1  X 2X+1 X^2+2X  X  1 X^2  2
 0  0 2X  0 2X^2  0  0 X^2 2X^2 X^2  0 2X^2 X^2+X X^2+X 2X^2+X 2X^2+2X X^2+2X 2X^2+X X^2+X 2X^2+X X^2+2X X^2  X 2X^2+2X 2X X^2+X X^2+2X 2X^2+2X 2X^2+2X 2X^2+X X^2+X 2X 2X  X 2X^2+2X X^2+2X 2X^2+2X 2X 2X 2X^2+X 2X 2X^2+X X^2+2X
 0  0  0  X 2X^2+X X^2+X X^2  X 2X^2+2X 2X X^2+2X X^2+2X X^2+2X X^2 2X^2+X X^2+X X^2+X X^2 2X^2+2X 2X X^2 X^2 X^2+X 2X  X X^2+2X 2X^2 2X^2+X X^2  0  0 2X^2 2X  X  X 2X^2+2X  0 X^2+2X 2X^2+2X  0  0 2X^2+X 2X^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+204x^77+404x^78+948x^79+1452x^80+1868x^81+3504x^82+3636x^83+4414x^84+8976x^85+6516x^86+6912x^87+9264x^88+4584x^89+2728x^90+1926x^91+816x^92+284x^93+132x^94+228x^95+118x^96+30x^97+48x^98+38x^99+6x^100+12x^101

The gray image is a linear code over GF(3) with n=387, k=10 and d=231.
This code was found by Heurico 1.16 in 5.82 seconds.