The generator matrix

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

generates a code of length 56 over Z3[X]/(X^3) who´s minimum homogenous weight is 103.

Homogenous weight enumerator: w(x)=1x^0+96x^103+168x^104+320x^105+726x^106+1008x^107+600x^108+1380x^109+2244x^110+1668x^111+2118x^112+3090x^113+1376x^114+1932x^115+1584x^116+608x^117+474x^118+96x^119+14x^120+72x^121+54x^122+8x^123+6x^124+18x^125+4x^126+10x^129+2x^132+2x^135+4x^141

The gray image is a linear code over GF(3) with n=504, k=9 and d=309.
This code was found by Heurico 1.16 in 3.51 seconds.