The generator matrix

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

generates a code of length 68 over Z3[X]/(X^3) who´s minimum homogenous weight is 127.

Homogenous weight enumerator: w(x)=1x^0+120x^127+348x^128+554x^129+684x^130+828x^131+1154x^132+1368x^133+1248x^134+2320x^135+2304x^136+1326x^137+2344x^138+1716x^139+1182x^140+1106x^141+510x^142+294x^143+24x^144+60x^145+90x^146+14x^147+30x^148+24x^149+4x^150+12x^151+6x^152+2x^159+4x^162+4x^165+2x^168

The gray image is a linear code over GF(3) with n=612, k=9 and d=381.
This code was found by Heurico 1.16 in 1.98 seconds.