The generator matrix

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

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+558x^163+1170x^164+2790x^165+3558x^166+5550x^167+8368x^168+6648x^169+10452x^170+12676x^171+11910x^172+14646x^173+16532x^174+13734x^175+15474x^176+16090x^177+9546x^178+8790x^179+8212x^180+4116x^181+3162x^182+1428x^183+690x^184+348x^185+202x^186+168x^187+102x^188+18x^189+60x^190+48x^191+20x^192+18x^193+30x^194+18x^196+6x^197+6x^199+2x^210

The gray image is a linear code over GF(3) with n=783, k=11 and d=489.
This code was found by Heurico 1.16 in 155 seconds.