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

generates a code of length 87 over Z3[X]/(X^3) who´s minimum homogenous weight is 167.

Homogenous weight enumerator: w(x)=1x^0+348x^167+224x^168+108x^169+672x^170+306x^171+324x^172+1260x^173+704x^174+324x^175+1170x^176+332x^177+216x^178+162x^179+46x^180+96x^182+38x^183+66x^185+20x^186+66x^188+14x^189+48x^191+14x^192+2x^234

The gray image is a linear code over GF(3) with n=783, k=8 and d=501.
This code was found by Heurico 1.16 in 95.7 seconds.