The generator matrix

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

generates a code of length 57 over Z3[X]/(X^3) who´s minimum homogenous weight is 106.

Homogenous weight enumerator: w(x)=1x^0+666x^106+990x^107+1732x^108+3480x^109+3312x^110+4462x^111+6564x^112+4572x^113+6094x^114+7200x^115+4896x^116+5058x^117+4434x^118+2358x^119+1238x^120+1350x^121+396x^122+80x^123+48x^124+40x^126+60x^127+6x^129+6x^130+6x^133

The gray image is a linear code over GF(3) with n=513, k=10 and d=318.
This code was found by Heurico 1.16 in 6.37 seconds.