The generator matrix

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

generates a code of length 87 over Z3[X]/(X^3) who´s minimum homogenous weight is 165.

Homogenous weight enumerator: w(x)=1x^0+612x^165+858x^166+1770x^167+3456x^168+2790x^169+3912x^170+5976x^171+3840x^172+3984x^173+6154x^174+3804x^175+3780x^176+5234x^177+3114x^178+2820x^179+3024x^180+1410x^181+1098x^182+862x^183+192x^184+102x^185+124x^186+18x^187+18x^188+44x^189+6x^190+12x^191+8x^192+6x^193+12x^195+6x^198+2x^201

The gray image is a linear code over GF(3) with n=783, k=10 and d=495.
This code was found by Heurico 1.16 in 10.3 seconds.