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

generates a code of length 47 over Z3[X]/(X^3) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+276x^85+330x^86+180x^87+540x^88+708x^89+586x^90+1176x^91+1950x^92+2100x^93+3294x^94+3132x^95+1924x^96+1302x^97+660x^98+214x^99+402x^100+330x^101+78x^102+228x^103+120x^104+18x^105+66x^106+54x^107+6x^109+6x^110+2x^123

The gray image is a linear code over GF(3) with n=423, k=9 and d=255.
This code was found by Heurico 1.16 in 1.77 seconds.