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

generates a code of length 80 over Z3[X]/(X^3) who´s minimum homogenous weight is 147.

Homogenous weight enumerator: w(x)=1x^0+70x^147+144x^148+114x^149+134x^150+348x^151+312x^152+280x^153+546x^154+408x^155+1296x^156+1356x^157+492x^158+3438x^159+2376x^160+606x^161+3450x^162+1728x^163+522x^164+628x^165+342x^166+246x^167+40x^168+228x^169+162x^170+28x^171+156x^172+42x^173+22x^174+48x^175+12x^176+30x^177+18x^178+24x^180+14x^183+8x^186+6x^189+4x^195+2x^201+2x^210

The gray image is a linear code over GF(3) with n=720, k=9 and d=441.
This code was found by Heurico 1.16 in 3.1 seconds.