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

generates a code of length 85 over Z3[X]/(X^3) who´s minimum homogenous weight is 163.

Homogenous weight enumerator: w(x)=1x^0+282x^163+348x^164+240x^165+594x^166+312x^167+618x^168+672x^169+366x^170+1034x^171+912x^172+204x^173+262x^174+300x^175+60x^176+4x^177+66x^178+42x^179+6x^180+48x^181+90x^182+12x^183+36x^184+24x^185+6x^188+6x^189+6x^191+6x^193+2x^201+2x^222

The gray image is a linear code over GF(3) with n=765, k=8 and d=489.
This code was found by Heurico 1.16 in 84.1 seconds.