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

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+146x^174+536x^177+972x^178+510x^180+16x^183+4x^186+2x^261

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 0.441 seconds.