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

generates a code of length 89 over Z3[X]/(X^3) who´s minimum homogenous weight is 174.

Homogenous weight enumerator: w(x)=1x^0+60x^174+36x^175+90x^176+148x^177+1548x^178+36x^179+194x^180+36x^181+36x^182+2x^267

The gray image is a linear code over GF(3) with n=801, k=7 and d=522.
This code was found by Heurico 1.16 in 0.331 seconds.