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

generates a code of length 72 over Z3[X]/(X^3) who´s minimum homogenous weight is 134.

Homogenous weight enumerator: w(x)=1x^0+366x^134+296x^135+72x^136+732x^137+450x^138+144x^139+1134x^140+1046x^141+2538x^142+1914x^143+1648x^144+3924x^145+1644x^146+1070x^147+612x^148+732x^149+240x^150+300x^152+194x^153+276x^155+96x^156+150x^158+40x^159+30x^161+12x^162+12x^164+2x^165+6x^168+2x^192

The gray image is a linear code over GF(3) with n=648, k=9 and d=402.
This code was found by Heurico 1.16 in 12 seconds.