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

generates a code of length 55 over Z3[X]/(X^3) who´s minimum homogenous weight is 101.

Homogenous weight enumerator: w(x)=1x^0+444x^101+300x^102+72x^103+1068x^104+540x^105+630x^106+1734x^107+1300x^108+1728x^109+3828x^110+2002x^111+1656x^112+1896x^113+516x^114+288x^115+678x^116+290x^117+348x^119+120x^120+150x^122+24x^123+54x^125+2x^126+6x^128+6x^129+2x^138

The gray image is a linear code over GF(3) with n=495, k=9 and d=303.
This code was found by Heurico 1.16 in 95.4 seconds.