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

generates a code of length 80 over Z3[X]/(X^3) who´s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+546x^150+36x^152+1170x^153+162x^154+180x^155+1806x^156+810x^157+864x^158+3504x^159+2268x^160+1476x^161+3386x^162+1134x^163+360x^164+726x^165+498x^168+368x^171+234x^174+114x^177+32x^180+6x^183+2x^216

The gray image is a linear code over GF(3) with n=720, k=9 and d=450.
This code was found by Heurico 1.16 in 6.22 seconds.