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

generates a code of length 81 over Z3[X]/(X^3) who´s minimum homogenous weight is 155.

Homogenous weight enumerator: w(x)=1x^0+294x^155+256x^156+180x^157+450x^158+606x^159+594x^160+438x^161+978x^162+864x^163+378x^164+678x^165+306x^166+144x^167+72x^168+84x^170+42x^171+78x^173+18x^174+42x^176+6x^177+18x^179+12x^180+6x^182+2x^183+12x^185+2x^216

The gray image is a linear code over GF(3) with n=729, k=8 and d=465.
This code was found by Heurico 1.16 in 39.4 seconds.