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

generates a code of length 89 over Z3[X]/(X^3) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+576x^168+18x^170+1238x^171+144x^172+252x^173+1728x^174+756x^175+1296x^176+2832x^177+2430x^178+2412x^179+2454x^180+1044x^181+396x^182+804x^183+450x^186+378x^189+258x^192+138x^195+58x^198+18x^201+2x^243

The gray image is a linear code over GF(3) with n=801, k=9 and d=504.
This code was found by Heurico 1.16 in 27.9 seconds.