The generator matrix

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

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+132x^163+450x^164+592x^165+1182x^166+1824x^167+2498x^168+3120x^169+3144x^170+3666x^171+5052x^172+4140x^173+5264x^174+6210x^175+5172x^176+4668x^177+3984x^178+2748x^179+2014x^180+1212x^181+666x^182+334x^183+300x^184+150x^185+68x^186+96x^187+78x^188+58x^189+60x^190+54x^191+12x^192+12x^193+18x^194+14x^195+18x^196+24x^197+6x^198+6x^199+2x^201

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 13.2 seconds.