The generator matrix

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

generates a code of length 56 over Z3[X]/(X^3) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+714x^105+450x^106+576x^107+1796x^108+1422x^109+1260x^110+2722x^111+2052x^112+1620x^113+2620x^114+1494x^115+882x^116+1334x^117+414x^118+36x^119+140x^120+68x^123+62x^126+18x^129+2x^144

The gray image is a linear code over GF(3) with n=504, k=9 and d=315.
This code was found by Heurico 1.16 in 1.07 seconds.