The generator matrix

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

generates a code of length 62 over Z3[X]/(X^3) who´s minimum homogenous weight is 115.

Homogenous weight enumerator: w(x)=1x^0+120x^115+198x^116+388x^117+888x^118+768x^119+854x^120+1650x^121+1338x^122+2104x^123+2640x^124+1722x^125+1896x^126+2262x^127+1062x^128+790x^129+600x^130+186x^131+10x^132+84x^133+42x^134+8x^135+18x^136+24x^137+10x^138+6x^140+8x^141+2x^150+2x^153+2x^156

The gray image is a linear code over GF(3) with n=558, k=9 and d=345.
This code was found by Heurico 1.16 in 26.5 seconds.