The generator matrix

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

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+396x^96+744x^97+1914x^98+3642x^99+5364x^100+5898x^101+9816x^102+13566x^103+13986x^104+19370x^105+21504x^106+18444x^107+19766x^108+17166x^109+10686x^110+7866x^111+3864x^112+1410x^113+968x^114+354x^115+90x^116+126x^117+96x^118+48x^119+12x^120+30x^121+12x^122+2x^123+6x^124

The gray image is a linear code over GF(3) with n=477, k=11 and d=288.
This code was found by Heurico 1.16 in 51.1 seconds.