The generator matrix

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

generates a code of length 71 over Z3[X]/(X^3) who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+136x^129+78x^131+336x^132+66x^133+222x^134+456x^135+324x^136+660x^137+1026x^138+1260x^139+1524x^140+2468x^141+2334x^142+1950x^143+2420x^144+1620x^145+1092x^146+504x^147+198x^148+174x^149+320x^150+30x^151+96x^152+188x^153+30x^155+78x^156+6x^158+32x^159+10x^162+16x^165+8x^168+12x^171+4x^174+2x^177+2x^186

The gray image is a linear code over GF(3) with n=639, k=9 and d=387.
This code was found by Heurico 1.16 in 2.64 seconds.