The generator matrix

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

generates a code of length 62 over Z3[X]/(X^3) who´s minimum homogenous weight is 118.

Homogenous weight enumerator: w(x)=1x^0+648x^118+1314x^119+1696x^120+2100x^121+1950x^122+1838x^123+1980x^124+1572x^125+1332x^126+1506x^127+1272x^128+798x^129+810x^130+516x^131+234x^132+72x^133+12x^134+2x^135+6x^136+6x^137+2x^138+6x^139+10x^141

The gray image is a linear code over GF(3) with n=558, k=9 and d=354.
This code was found by Heurico 1.16 in 0.816 seconds.