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

generates a code of length 62 over Z3[X]/(X^3) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+416x^114+54x^116+948x^117+108x^118+432x^119+1518x^120+648x^121+2268x^122+2456x^123+1296x^124+3672x^125+2328x^126+864x^127+864x^128+716x^129+592x^132+276x^135+158x^138+62x^141+2x^147+2x^150+2x^162

The gray image is a linear code over GF(3) with n=558, k=9 and d=342.
This code was found by Heurico 1.16 in 1.96 seconds.