The generator matrix

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

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+182x^114+372x^115+804x^116+1328x^117+1608x^118+2460x^119+3540x^120+3660x^121+5190x^122+6356x^123+5868x^124+7182x^125+6514x^126+4680x^127+4110x^128+2620x^129+876x^130+492x^131+438x^132+252x^133+96x^134+82x^135+102x^136+54x^137+50x^138+72x^139+24x^140+26x^141+6x^142+4x^144

The gray image is a linear code over GF(3) with n=558, k=10 and d=342.
This code was found by Heurico 1.16 in 8.93 seconds.