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  X  1  1  1  1  1  1  1  1  1  X  X  X  1  1  0  X  1  1  1
 0  X  0  0 2X 2X^2+X 2X^2+2X  X 2X 2X^2+X 2X^2  0 2X 2X^2 2X^2+X X^2+2X 2X^2+2X 2X^2+X 2X^2+2X 2X^2 2X 2X^2  X X^2+2X 2X^2  0 X^2+X 2X^2  X 2X X^2  X X^2+X 2X^2+2X 2X^2+X 2X 2X^2 2X^2+X 2X 2X^2+2X 2X^2+2X 2X^2+2X  X 2X X^2+X  0 2X^2
 0  0  X 2X  0 X^2+2X X^2+X  X X^2+2X 2X^2+2X  X X^2+2X 2X X^2 X^2 X^2+X X^2  X 2X^2+X X^2 2X^2 X^2 2X^2 X^2+2X  X 2X 2X^2 2X^2+X 2X^2+X 2X^2+2X X^2+2X 2X^2+2X  0  0 X^2+X X^2 2X^2+X 2X^2+2X X^2 2X^2+X X^2+X X^2+X X^2+2X X^2 X^2+X X^2 X^2+X
 0  0  0 X^2  0  0 2X^2  0  0 X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2  0  0 2X^2 2X^2 2X^2 2X^2  0 X^2 X^2  0 2X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 2X^2 2X^2  0  0  0  0 X^2 X^2 2X^2 2X^2
 0  0  0  0 X^2 2X^2  0 X^2 2X^2  0 2X^2 2X^2 2X^2  0  0 X^2 2X^2 2X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 X^2  0 X^2  0  0 X^2  0 X^2 2X^2  0  0 X^2  0 X^2  0 2X^2  0  0 X^2 2X^2  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+154x^84+48x^85+192x^86+568x^87+336x^88+420x^89+980x^90+996x^91+2610x^92+1950x^93+1566x^94+4740x^95+1844x^96+1182x^97+552x^98+520x^99+144x^100+162x^101+356x^102+78x^103+54x^104+120x^105+12x^106+18x^107+56x^108+12x^109+6x^111+4x^114+2x^123

The gray image is a linear code over GF(3) with n=423, k=9 and d=252.
This code was found by Heurico 1.16 in 1.38 seconds.