The generator matrix

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

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+174x^105+126x^106+306x^107+796x^108+864x^109+738x^110+1760x^111+1926x^112+1224x^113+2456x^114+2844x^115+1476x^116+2144x^117+1458x^118+558x^119+452x^120+72x^121+72x^122+154x^123+46x^126+16x^129+6x^132+10x^135+4x^138

The gray image is a linear code over GF(3) with n=513, k=9 and d=315.
This code was found by Heurico 1.16 in 1.02 seconds.