The generator matrix

 1  0  1  1  1  1  1  1  0  1  1 2X^2+X 2X  1  1  1  1  1  1  1  1  1 2X^2+X  1 2X  1  1  1 2X^2  1  1  X  1 2X  1  1  1  1 X^2+2X  1 2X^2  1  1  1  1 2X^2+2X  1  1  1  1  1  1  1  1  1 X^2 X^2  1  1  1  1  1
 0  1  1  2 2X^2+X 2X^2+X+2 2X^2+2X+1 2X  1  2 2X^2+X+1  1  1 2X^2+2X+1 X+1 2X^2 2X+2 2X+1  1 2X^2+X+2  X 2X+2  1 2X^2+2X  1 2X^2+2 X+2  X  1 X+1 X^2+X  1 2X  1 X^2+X+2 X+1 X^2+2X+2 2X^2  1 2X  1  2 X^2+2X 2X^2 2X^2+2X+1  1  2 2X^2+2 X^2+X+2 X^2+X+2 X^2+2X 2X^2+2X 2X+2  X 2X^2+X+2  1  0 2X 2X^2+2 2X+2  X X^2+X
 0  0 2X  0 2X^2 2X^2 X^2  0 2X^2+2X X^2+2X  X 2X^2+2X X^2+2X 2X^2+2X 2X^2+2X X^2+X X^2+2X  X 2X^2+X 2X  X 2X^2 2X^2  X 2X^2 X^2+X X^2+X 2X^2+X  X 2X X^2  X X^2+2X  0 X^2+2X X^2 2X^2+X 2X^2+2X 2X^2+2X 2X^2 2X 2X^2+2X  0  X 2X^2+X 2X 2X^2 X^2 X^2+X  0 X^2+X X^2+X  X X^2+2X 2X^2 2X^2+X  X X^2 2X  X  X 2X^2+X
 0  0  0 X^2 X^2  0 2X^2 2X^2 X^2  0 X^2 2X^2  0 2X^2 X^2  0 2X^2  0 2X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2 X^2  0 2X^2  0  0 X^2 X^2  0  0 X^2 X^2 2X^2 X^2 X^2 2X^2 X^2  0 2X^2 X^2  0  0  0 2X^2 2X^2 2X^2  0  0 2X^2 2X^2 2X^2 X^2 X^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 117.

Homogenous weight enumerator: w(x)=1x^0+700x^117+774x^118+414x^119+1908x^120+1620x^121+792x^122+2628x^123+2394x^124+1080x^125+2686x^126+1926x^127+612x^128+1152x^129+486x^130+18x^131+210x^132+90x^133+136x^135+18x^138+24x^141+10x^144+4x^153

The gray image is a linear code over GF(3) with n=558, k=9 and d=351.
This code was found by Heurico 1.16 in 4.1 seconds.