The generator matrix

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

generates a code of length 66 over Z3[X]/(X^3) who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+858x^124+1218x^125+2294x^126+3486x^127+3882x^128+4272x^129+5628x^130+4974x^131+5658x^132+6348x^133+4296x^134+4396x^135+4608x^136+2934x^137+1806x^138+1224x^139+600x^140+246x^141+168x^142+48x^143+32x^144+24x^145+24x^146+6x^147+6x^148+6x^149+6x^151

The gray image is a linear code over GF(3) with n=594, k=10 and d=372.
This code was found by Heurico 1.16 in 64.2 seconds.