The generator matrix

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

generates a code of length 87 over Z3[X]/(X^3) who´s minimum homogenous weight is 163.

Homogenous weight enumerator: w(x)=1x^0+300x^163+516x^164+606x^165+1446x^166+1200x^167+2296x^168+3294x^169+2556x^170+4398x^171+5244x^172+3618x^173+5804x^174+6336x^175+3864x^176+5586x^177+4686x^178+1836x^179+2170x^180+1518x^181+522x^182+246x^183+288x^184+210x^185+16x^186+114x^187+144x^188+8x^189+66x^190+96x^191+2x^192+30x^193+18x^194+6x^196+4x^204+2x^207+2x^210

The gray image is a linear code over GF(3) with n=783, k=10 and d=489.
This code was found by Heurico 1.16 in 65.3 seconds.