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

generates a code of length 55 over Z3[X]/(X^3) who´s minimum homogenous weight is 100.

Homogenous weight enumerator: w(x)=1x^0+528x^100+810x^101+1748x^102+4266x^103+5052x^104+6438x^105+11058x^106+11628x^107+13256x^108+20862x^109+19560x^110+17752x^111+22758x^112+15120x^113+10036x^114+8718x^115+3738x^116+1878x^117+1140x^118+342x^119+132x^120+120x^121+96x^122+26x^123+42x^124+24x^125+6x^126+6x^127+6x^128

The gray image is a linear code over GF(3) with n=495, k=11 and d=300.
This code was found by Heurico 1.16 in 55.4 seconds.