The generator matrix

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

generates a code of length 62 over Z3[X]/(X^3) who´s minimum homogenous weight is 113.

Homogenous weight enumerator: w(x)=1x^0+1032x^113+1920x^114+4050x^115+8442x^116+11634x^117+14862x^118+23736x^119+29192x^120+34896x^121+45384x^122+51972x^123+51720x^124+59418x^125+56934x^126+43530x^127+38310x^128+24332x^129+13932x^130+9288x^131+3720x^132+1704x^133+882x^134+284x^135+36x^136+90x^137+62x^138+24x^139+42x^140+6x^141+6x^144

The gray image is a linear code over GF(3) with n=558, k=12 and d=339.
This code was found by Heurico 1.16 in 513 seconds.