The generator matrix

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

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+228x^102+240x^103+684x^104+1460x^105+1086x^106+3078x^107+3434x^108+2406x^109+6522x^110+7184x^111+3786x^112+8802x^113+6944x^114+3282x^115+5082x^116+2780x^117+696x^118+522x^119+288x^120+78x^121+54x^122+192x^123+60x^124+30x^125+72x^126+30x^127+12x^128+4x^129+8x^132+4x^135

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 8.1 seconds.