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  X  X  X  0  0  0  1  1  1  1  X  X  X  0  0  0  1  1  1  1  X  X  0  0  X  0  1  1  1  1  X  X  0  X  0  X  0  X  1  1  1  1  X  X  X  0  0  X  0  X  1  1  1  X  0  X  0  X  X  0
 0  X  0  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  X  X  X  X  0  0  0  X  X  0  X  X  X  X  0  0  0  X  X  0  X  X  0  X  X  0  0  X  X  0  0  0  X  X  X  X  0  0  0  X  X  0  0  X  X  0  X  X  0  0  0  X  0  0  X  X  0  X  X
 0  0  X  X  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  X  X  0  0  X  X  0  X  X  0  X  X  0  0  X  X  0  X  X  0  X  X  X  X  0  0  0  X  X  0  0  X  X  X  X  0  0  0  0  X  X  0  0  X  X  X  X  0  0  0  0  X  X  X  X  X  X  0  0  0

generates a code of length 88 over Z2[X]/(X^2) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+8x^93+4x^94+3x^96

The gray image is a linear code over GF(2) with n=176, k=4 and d=93.
As d=93 is an upper bound for linear (176,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.127 seconds.