The generator matrix

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

generates a code of length 57 over Z3[X]/(X^3) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+654x^105+396x^106+918x^107+2184x^108+2430x^109+2826x^110+3942x^111+5508x^112+6318x^113+6162x^114+7758x^115+6804x^116+4530x^117+3888x^118+2088x^119+1344x^120+432x^121+480x^123+294x^126+78x^129+12x^132+2x^135

The gray image is a linear code over GF(3) with n=513, k=10 and d=315.
This code was found by Heurico 1.16 in 31.5 seconds.