The generator matrix

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

generates a code of length 72 over Z3[X]/(X^3) who´s minimum homogenous weight is 136.

Homogenous weight enumerator: w(x)=1x^0+390x^136+318x^137+672x^138+1362x^139+1098x^140+1502x^141+2262x^142+1260x^143+1364x^144+3012x^145+1326x^146+1382x^147+1572x^148+672x^149+552x^150+498x^151+114x^152+90x^153+78x^154+30x^155+8x^156+36x^157+30x^158+8x^159+12x^160+12x^161+6x^162+12x^163+2x^165+2x^168

The gray image is a linear code over GF(3) with n=648, k=9 and d=408.
This code was found by Heurico 1.16 in 1.47 seconds.