The generator matrix

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

generates a code of length 62 over Z3[X]/(X^3) who´s minimum homogenous weight is 117.

Homogenous weight enumerator: w(x)=1x^0+372x^117+18x^118+54x^119+678x^120+108x^121+486x^122+1044x^123+1188x^124+810x^125+1026x^126+144x^127+108x^128+216x^129+120x^132+116x^135+60x^138+6x^141+4x^144+2x^171

The gray image is a linear code over GF(3) with n=558, k=8 and d=351.
This code was found by Heurico 1.16 in 0.431 seconds.