The generator matrix

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

generates a code of length 66 over Z3[X]/(X^3) who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+168x^123+456x^124+1974x^125+1902x^126+2628x^127+4986x^128+3548x^129+4248x^130+8178x^131+4238x^132+4566x^133+7890x^134+3646x^135+2940x^136+3804x^137+1322x^138+1062x^139+834x^140+378x^141+108x^142+18x^143+64x^144+12x^145+12x^146+32x^147+18x^148+6x^149+10x^150

The gray image is a linear code over GF(3) with n=594, k=10 and d=369.
This code was found by Heurico 1.16 in 7.75 seconds.