The generator matrix

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

generates a code of length 76 over Z3[X]/(X^3) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+288x^144+270x^145+1014x^146+1050x^147+1116x^148+2088x^149+1388x^150+1674x^151+2268x^152+1718x^153+1290x^154+1944x^155+1224x^156+864x^157+804x^158+260x^159+108x^160+84x^161+62x^162+24x^163+18x^164+30x^165+24x^167+24x^168+6x^170+14x^171+12x^173+6x^174+8x^177+2x^180

The gray image is a linear code over GF(3) with n=684, k=9 and d=432.
This code was found by Heurico 1.16 in 1.59 seconds.