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

generates a code of length 47 over Z3[X]/(X^3) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+122x^87+204x^88+138x^89+274x^90+354x^91+438x^92+568x^93+2418x^94+750x^95+558x^96+276x^97+60x^98+50x^99+36x^100+48x^101+80x^102+48x^103+24x^104+38x^105+60x^106+8x^108+6x^109+2x^132

The gray image is a linear code over GF(3) with n=423, k=8 and d=261.
This code was found by Heurico 1.16 in 0.19 seconds.