The generator matrix

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

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+404x^102+834x^103+2172x^104+3996x^105+4872x^106+7458x^107+10644x^108+11358x^109+15480x^110+18916x^111+16794x^112+20802x^113+20184x^114+15228x^115+12108x^116+8570x^117+3420x^118+2088x^119+990x^120+372x^121+102x^122+144x^123+60x^124+36x^125+42x^126+36x^127+18x^128+18x^129

The gray image is a linear code over GF(3) with n=504, k=11 and d=306.
This code was found by Heurico 1.16 in 56.7 seconds.