The generator matrix

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

generates a code of length 48 over Z3[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+1008x^86+2114x^87+5328x^88+9306x^89+12948x^90+20124x^91+28182x^92+36640x^93+46800x^94+58140x^95+61078x^96+67602x^97+63450x^98+46950x^99+33630x^100+20772x^101+9992x^102+4734x^103+1800x^104+528x^105+96x^106+54x^107+74x^108+48x^109+24x^110+12x^111+6x^114

The gray image is a linear code over GF(3) with n=432, k=12 and d=258.
This code was found by Heurico 1.16 in 368 seconds.