The generator matrix

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

generates a code of length 47 over Z3[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+390x^86+434x^87+1866x^88+2580x^89+3582x^90+5826x^91+4086x^92+6080x^93+8058x^94+5394x^95+6654x^96+6690x^97+3336x^98+1844x^99+1278x^100+666x^101+94x^102+78x^103+48x^104+20x^105+12x^106+24x^107+6x^109+2x^114

The gray image is a linear code over GF(3) with n=423, k=10 and d=258.
This code was found by Heurico 1.16 in 5.26 seconds.