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

generates a code of length 63 over Z3[X]/(X^3) who´s minimum homogenous weight is 119.

Homogenous weight enumerator: w(x)=1x^0+282x^119+158x^120+624x^122+456x^123+162x^124+960x^125+1596x^126+324x^127+1134x^128+292x^129+180x^131+66x^132+114x^134+62x^135+60x^137+34x^138+42x^140+6x^143+6x^144+2x^174

The gray image is a linear code over GF(3) with n=567, k=8 and d=357.
This code was found by Heurico 1.16 in 2 seconds.