The generator matrix

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

generates a code of length 62 over Z3[X]/(X^3) who´s minimum homogenous weight is 121.

Homogenous weight enumerator: w(x)=1x^0+390x^121+408x^122+8x^123+768x^124+198x^125+8x^126+102x^127+144x^128+4x^129+144x^130+6x^131+2x^138+4x^141

The gray image is a linear code over GF(3) with n=558, k=7 and d=363.
This code was found by Heurico 1.16 in 0.0895 seconds.