The generator matrix

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

generates a code of length 89 over Z3[X]/(X^3) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+864x^168+432x^169+576x^170+2884x^171+2070x^172+2196x^173+4230x^174+3474x^175+3996x^176+5880x^177+4698x^178+5346x^179+5750x^180+4950x^181+3096x^182+4056x^183+1656x^184+810x^185+996x^186+216x^187+18x^188+366x^189+228x^192+144x^195+96x^198+18x^201+2x^207

The gray image is a linear code over GF(3) with n=801, k=10 and d=504.
This code was found by Heurico 1.16 in 20.1 seconds.