The generator matrix

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

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+294x^118+216x^119+556x^120+792x^121+648x^122+416x^123+780x^124+648x^125+378x^126+750x^127+432x^128+308x^129+282x^130+28x^132+12x^133+6x^135+6x^139+4x^141+2x^144+2x^159

The gray image is a linear code over GF(3) with n=558, k=8 and d=354.
This code was found by Heurico 1.16 in 5.54 seconds.