The generator matrix

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

generates a code of length 69 over Z3[X]/(X^3) who´s minimum homogenous weight is 127.

Homogenous weight enumerator: w(x)=1x^0+246x^127+528x^128+1708x^129+3342x^130+3996x^131+6034x^132+8028x^133+9954x^134+11676x^135+15204x^136+16752x^137+17070x^138+17628x^139+17274x^140+14550x^141+12636x^142+8016x^143+5514x^144+3462x^145+1638x^146+872x^147+534x^148+96x^149+116x^150+90x^151+42x^152+44x^153+60x^154+18x^155+6x^156+6x^157+6x^161

The gray image is a linear code over GF(3) with n=621, k=11 and d=381.
This code was found by Heurico 1.16 in 72.3 seconds.