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

generates a code of length 53 over Z3[X]/(X^3) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+126x^96+258x^97+138x^98+326x^99+684x^100+492x^101+772x^102+1944x^103+1074x^104+1588x^105+4500x^106+1926x^107+1630x^108+2142x^109+546x^110+292x^111+276x^112+132x^113+232x^114+246x^115+60x^116+86x^117+126x^118+6x^119+30x^120+30x^121+16x^123+2x^129+2x^138

The gray image is a linear code over GF(3) with n=477, k=9 and d=288.
This code was found by Heurico 1.16 in 1.61 seconds.