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

generates a code of length 56 over Z3[X]/(X^3) who´s minimum homogenous weight is 106.

Homogenous weight enumerator: w(x)=1x^0+702x^106+1050x^107+1046x^108+2958x^109+1914x^110+1158x^111+2814x^112+1734x^113+1012x^114+2178x^115+966x^116+462x^117+1038x^118+486x^119+114x^120+18x^121+2x^123+6x^124+6x^125+6x^126+6x^127+6x^129

The gray image is a linear code over GF(3) with n=504, k=9 and d=318.
This code was found by Heurico 1.16 in 0.709 seconds.