The generator matrix

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

generates a code of length 47 over Z3[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+894x^84+2130x^85+5640x^86+8420x^87+12798x^88+20070x^89+26044x^90+37278x^91+50298x^92+54584x^93+63210x^94+73044x^95+57848x^96+48414x^97+34680x^98+19406x^99+9720x^100+4722x^101+1570x^102+360x^103+84x^104+68x^105+60x^106+24x^107+50x^108+18x^109+6x^110

The gray image is a linear code over GF(3) with n=423, k=12 and d=252.
This code was found by Heurico 1.16 in 356 seconds.