The generator matrix

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

generates a code of length 68 over Z3[X]/(X^3) who´s minimum homogenous weight is 126.

Homogenous weight enumerator: w(x)=1x^0+244x^126+582x^127+648x^128+1452x^129+2610x^130+2268x^131+3222x^132+4188x^133+4446x^134+5430x^135+6876x^136+5742x^137+6246x^138+5340x^139+3726x^140+2408x^141+1488x^142+630x^143+460x^144+492x^145+36x^146+114x^147+168x^148+74x^150+84x^151+30x^153+24x^154+18x^157+2x^159

The gray image is a linear code over GF(3) with n=612, k=10 and d=378.
This code was found by Heurico 1.16 in 15.3 seconds.