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

generates a code of length 89 over Z3[X]/(X^3) who´s minimum homogenous weight is 171.

Homogenous weight enumerator: w(x)=1x^0+452x^171+126x^172+252x^173+790x^174+306x^175+378x^176+948x^177+540x^178+486x^179+828x^180+414x^181+288x^182+278x^183+72x^184+54x^185+106x^186+74x^189+96x^192+44x^195+18x^198+6x^201+2x^207+2x^225

The gray image is a linear code over GF(3) with n=801, k=8 and d=513.
This code was found by Heurico 1.16 in 5.08 seconds.