The generator matrix

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

generates a code of length 58 over Z3[X]/(X^3) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+90x^105+66x^106+462x^107+622x^108+978x^109+1944x^110+2496x^111+2466x^112+4368x^113+5622x^114+5214x^115+7662x^116+7548x^117+5058x^118+5736x^119+4098x^120+1968x^121+1368x^122+440x^123+192x^124+192x^125+116x^126+84x^127+114x^128+66x^129+12x^130+6x^131+20x^132+18x^134+18x^135+2x^141+2x^144

The gray image is a linear code over GF(3) with n=522, k=10 and d=315.
This code was found by Heurico 1.16 in 8.74 seconds.