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

generates a code of length 88 over Z3[X]/(X^2) who´s minimum homogenous weight is 173.

Homogenous weight enumerator: w(x)=1x^0+108x^173+30x^174+36x^177+6x^180+54x^182+4x^183+2x^189+2x^237

The gray image is a linear code over GF(3) with n=264, k=5 and d=173.
This code was found by Heurico 1.16 in 0.666 seconds.