The generator matrix

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

generates a code of length 62 over Z3[X]/(X^3) who´s minimum homogenous weight is 116.

Homogenous weight enumerator: w(x)=1x^0+708x^116+1088x^117+2196x^118+3600x^119+3182x^120+4500x^121+6840x^122+4122x^123+5598x^124+7320x^125+3998x^126+4608x^127+4968x^128+2330x^129+1872x^130+1206x^131+546x^132+180x^133+72x^134+16x^135+54x^137+14x^138+18x^140+12x^141

The gray image is a linear code over GF(3) with n=558, k=10 and d=348.
This code was found by Heurico 1.16 in 7.08 seconds.