The generator matrix

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

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+276x^167+226x^168+696x^170+568x^171+108x^172+828x^173+1472x^174+648x^175+1560x^176+2898x^177+1296x^178+2154x^179+3082x^180+864x^181+804x^182+810x^183+330x^185+166x^186+324x^188+112x^189+132x^191+72x^192+126x^194+22x^195+48x^197+44x^198+2x^201+12x^203+2x^237

The gray image is a linear code over GF(3) with n=801, k=9 and d=501.
This code was found by Heurico 1.16 in 3.19 seconds.