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

generates a code of length 88 over Z3[X]/(X^3) who´s minimum homogenous weight is 167.

Homogenous weight enumerator: w(x)=1x^0+480x^167+1022x^168+2352x^169+2586x^170+3322x^171+4440x^172+4134x^173+4146x^174+5604x^175+4362x^176+4602x^177+5082x^178+4020x^179+2986x^180+3462x^181+2130x^182+1688x^183+1134x^184+648x^185+394x^186+246x^187+66x^188+42x^189+18x^190+24x^191+10x^192+12x^193+6x^195+6x^196+6x^197+6x^198+12x^200

The gray image is a linear code over GF(3) with n=792, k=10 and d=501.
This code was found by Heurico 1.16 in 10.5 seconds.