The generator matrix

 1  0  0  1  1  1  1  1 2X  1  1  1 X^2  1  1  1 2X^2+2X  1 2X^2  1  1 X^2  1  X  1  1  1  0 2X^2+2X  1  1  1  1  1 X^2+X  1  1  1  1  X  1  X 2X^2+2X  1  1  1  1  1  1  1 X^2+2X  1 X^2+2X  1 X^2+X  0
 0  1  0  0 2X^2+X 2X+1  2  1  1 X^2+2X+1 2X^2+X+2 2X^2+2X+2  1 2X+1 X^2  2  1 X^2+X X^2+X 2X^2+X 2X^2+2X+2  1 X^2+2  1 X^2+1 X^2+X+1 2X+2  1 X^2 2X+1 X^2 X^2+X+1 2X^2+X+2 2X^2+X+1  1 2X^2+2X+1 2X^2+2 X^2+2X+1  2  1 2X  1  1 2X 2X^2+X X^2+2X+2  1 X^2+2 X+2  1  1 2X^2+2  1 X^2+2X+1  1  1
 0  0  1 2X^2+2X+1 2X^2+2X+2 X+2  2  1 X+1 2X^2+X 2X^2 X^2+2X+1 2X^2+2 X^2+2X+1 2X^2+2X 2X^2 X^2+X+2 2X^2+X+2  1 2X^2+2X+1 2X^2+1 2X^2+X X^2+2X X^2+2X+1 2X  2 2X^2+2 X^2+2X+2  1  1 2X^2+X+1 2X^2+2X X^2+X+1 2X^2+2X+2 X^2+1 2X^2+X+1 2X^2+X+2  2 X^2+X  X X^2+1 2X^2+2 2X^2+1 X^2+2 X^2+2  0 X^2+X+1 2X+1 2X^2+1 2X^2+X 2X^2+2X  X  0 X^2 2X+1 2X
 0  0  0 2X^2 2X^2 2X^2 2X^2 2X^2  0 2X^2 2X^2 2X^2  0  0 X^2 X^2 X^2  0 2X^2 X^2  0 2X^2  0 X^2 X^2 X^2  0 2X^2  0 X^2 2X^2  0 X^2  0 2X^2 X^2 X^2  0 X^2 X^2  0 2X^2 X^2 X^2  0 2X^2 2X^2  0 X^2  0 X^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 104.

Homogenous weight enumerator: w(x)=1x^0+612x^104+632x^105+1890x^106+3420x^107+3354x^108+5598x^109+5850x^110+4060x^111+6924x^112+6828x^113+4460x^114+5658x^115+4368x^116+1904x^117+1692x^118+1170x^119+348x^120+96x^121+84x^122+44x^123+12x^124+6x^125+12x^126+18x^128+8x^129

The gray image is a linear code over GF(3) with n=504, k=10 and d=312.
This code was found by Heurico 1.16 in 6.28 seconds.