The generator matrix

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

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+378x^85+528x^86+818x^87+1632x^88+2640x^89+2982x^90+3942x^91+5256x^92+6834x^93+6450x^94+7734x^95+7090x^96+5166x^97+3474x^98+1814x^99+1074x^100+570x^101+92x^102+228x^103+144x^104+48x^105+78x^106+60x^107+6x^109+6x^110+4x^111

The gray image is a linear code over GF(3) with n=423, k=10 and d=255.
This code was found by Heurico 1.16 in 39.8 seconds.