The generator matrix

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

generates a code of length 55 over Z3[X]/(X^3) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+720x^104+804x^105+1302x^106+2970x^107+1706x^108+1656x^109+2514x^110+1402x^111+1266x^112+2370x^113+748x^114+696x^115+942x^116+426x^117+90x^118+24x^119+14x^120+12x^121+6x^122+2x^123+12x^125

The gray image is a linear code over GF(3) with n=495, k=9 and d=312.
This code was found by Heurico 1.16 in 0.693 seconds.