The generator matrix

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

generates a code of length 72 over Z3[X]/(X^2) who´s minimum homogenous weight is 129.

Homogenous weight enumerator: w(x)=1x^0+78x^129+54x^130+276x^131+318x^132+276x^133+636x^134+732x^135+504x^136+1044x^137+794x^138+606x^139+1302x^140+944x^141+660x^142+1428x^143+1044x^144+636x^145+1230x^146+890x^147+648x^148+1314x^149+726x^150+540x^151+864x^152+488x^153+264x^154+468x^155+300x^156+150x^157+132x^158+144x^159+36x^160+42x^161+54x^162+12x^164+22x^165+10x^168+10x^171+4x^174+2x^180

The gray image is a linear code over GF(3) with n=216, k=9 and d=129.
This code was found by Heurico 1.16 in 6.92 seconds.