The generator matrix

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

generates a code of length 69 over Z3[X]/(X^3) who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+140x^129+108x^130+702x^131+970x^132+372x^133+1764x^134+1158x^135+396x^136+3234x^137+2248x^138+528x^139+3414x^140+1808x^141+348x^142+1470x^143+564x^144+126x^145+60x^146+70x^147+48x^148+42x^149+60x^150+18x^151+6x^152+12x^153+8x^156+2x^159+2x^162+4x^168

The gray image is a linear code over GF(3) with n=621, k=9 and d=387.
This code was found by Heurico 1.16 in 1.32 seconds.