The generator matrix

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

generates a code of length 89 over Z3[X]/(X^3) who´s minimum homogenous weight is 167.

Homogenous weight enumerator: w(x)=1x^0+1050x^167+1206x^168+2412x^169+4122x^170+4794x^171+6660x^172+9888x^173+9688x^174+11106x^175+14340x^176+13620x^177+14616x^178+16776x^179+13506x^180+14076x^181+12576x^182+8668x^183+6498x^184+5100x^185+2670x^186+1386x^187+1278x^188+368x^189+108x^190+312x^191+94x^192+96x^194+36x^195+36x^197+24x^198+30x^200+6x^203

The gray image is a linear code over GF(3) with n=801, k=11 and d=501.
This code was found by Heurico 1.16 in 98.8 seconds.