The generator matrix

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

generates a code of length 87 over Z3[X]/(X^3) who´s minimum homogenous weight is 159.

Homogenous weight enumerator: w(x)=1x^0+64x^159+18x^160+66x^161+218x^162+162x^163+426x^164+1006x^165+876x^166+1578x^167+2096x^168+2430x^169+2916x^170+4248x^171+4392x^172+4932x^173+5344x^174+6180x^175+5166x^176+5174x^177+3630x^178+3012x^179+2178x^180+1164x^181+744x^182+488x^183+72x^184+60x^185+170x^186+24x^187+54x^188+80x^189+6x^190+24x^192+10x^195+8x^198+12x^201+6x^204+2x^207+2x^210+2x^213+6x^216+2x^222

The gray image is a linear code over GF(3) with n=783, k=10 and d=477.
This code was found by Heurico 1.16 in 14 seconds.