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  X  1  X  1  X  1  X  1  1  1  1  X  X  X  X  0  1  1  1  1  1  1
 0  X  0  0  X  0  X  X 2X  0  0  X  X  0 2X  X 2X 2X  0  X 2X  0  X 2X 2X 2X 2X  0  0  0  X  X  0  X  X 2X  0  0  X  X  0 2X  X 2X 2X  0  X 2X  0  X 2X 2X 2X 2X  0  0  0  X  X  0  X  X 2X  0  0  X  X  X  0  X 2X 2X  0  X  X  0  X  X 2X  X 2X 2X  X 2X 2X 2X 2X 2X 2X
 0  0  X  0 2X  X 2X  X 2X  0  X  X  0 2X  0  0  X  X 2X 2X 2X 2X  X  0  0  X 2X  0  0  X 2X  X  X 2X  0 2X  0  X  X  0 2X  0  0  X  X 2X 2X 2X 2X  X  0  0  X 2X  0  0  X 2X  X  X 2X  0 2X  0  X  X  0  0 2X 2X  X 2X 2X  X 2X 2X  X  0 2X 2X  0  0 2X  0  0  X 2X  0  X
 0  0  0  X 2X 2X  0 2X 2X 2X  X  0 2X  0 2X  X  X  0  X  X  X 2X  X  0  X 2X  0  0  X 2X 2X 2X  X  X  X 2X 2X  0  0  0  X  X 2X 2X  X  0  0  0 2X  X  0 2X  0  X  0  X 2X 2X 2X  X  X  X 2X 2X  0  0  0 2X  X  0  0 2X  0 2X  0 2X  X 2X  0  X 2X  0 2X  0 2X 2X  0  X  X

generates a code of length 89 over Z3[X]/(X^2) who´s minimum homogenous weight is 175.

Homogenous weight enumerator: w(x)=1x^0+108x^175+48x^177+24x^180+54x^184+4x^186+2x^189+2x^240

The gray image is a linear code over GF(3) with n=267, k=5 and d=175.
This code was found by Heurico 1.16 in 0.337 seconds.