The generator matrix

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

generates a code of length 55 over Z3[X]/(X^3) who´s minimum homogenous weight is 99.

Homogenous weight enumerator: w(x)=1x^0+404x^99+1212x^100+3708x^101+6102x^102+11274x^103+14604x^104+21548x^105+28890x^106+34236x^107+44904x^108+57768x^109+56232x^110+62528x^111+60894x^112+44646x^113+34816x^114+23532x^115+13002x^116+6498x^117+2922x^118+1110x^119+292x^120+102x^121+78x^122+48x^123+30x^124+48x^125+6x^126+6x^128

The gray image is a linear code over GF(3) with n=495, k=12 and d=297.
This code was found by Heurico 1.16 in 427 seconds.