The generator matrix

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

generates a code of length 56 over Z3[X]/(X^3) who´s minimum homogenous weight is 102.

Homogenous weight enumerator: w(x)=1x^0+198x^102+180x^103+462x^104+1622x^105+1722x^106+2298x^107+3516x^108+3942x^109+4380x^110+6884x^111+6540x^112+6624x^113+7040x^114+5508x^115+3102x^116+2566x^117+876x^118+510x^119+464x^120+114x^121+78x^122+194x^123+42x^124+36x^125+100x^126+24x^127+6x^128+14x^129+6x^130

The gray image is a linear code over GF(3) with n=504, k=10 and d=306.
This code was found by Heurico 1.16 in 7.88 seconds.