The generator matrix

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

generates a code of length 55 over Z3[X]/(X^3) who´s minimum homogenous weight is 103.

Homogenous weight enumerator: w(x)=1x^0+432x^103+648x^104+846x^105+1584x^106+1254x^107+1264x^108+2730x^109+2022x^110+1906x^111+2946x^112+1392x^113+912x^114+888x^115+432x^116+160x^117+60x^118+48x^119+10x^120+78x^121+30x^122+30x^124+6x^125+2x^129+2x^138

The gray image is a linear code over GF(3) with n=495, k=9 and d=309.
This code was found by Heurico 1.16 in 82.2 seconds.