The generator matrix

 1  0  1  1  1  0  1  1  X  1  1  X  1  1  0  1  1  0  1  1  X  1  1  X  1  1  0  1  1  0  1  1  X  1  1  X  1  1  1  1  1  1  1  1  X  X  0  0  0  X  0  X  1  1  1  1  1  1  1  1  X  X  0  X  X  0  0  0  X  0  X  X  X  0  1  1  1  1  1  1  1  1  X  X  X  X  1
 0  1  1  0 X+1  1  X X+1  1  X  1  1  0 X+1  1  0 X+1  1  X  1  1  X  1  1  0 X+1  1  0 X+1  1  X  1  1  X  1  1  0  0 X+1 X+1  X  X  1  1  0  X  X  0  1  1  1  1  0  X  0  X X+1  1 X+1  1  0  X  X  0  X  X  0  1  1  1  1  0  X  X  0  0  X  X X+1 X+1  1  1  0  X  0  X  0
 0  0  X  X  0  X  X  X  X  0  0  0  0  0  X  X  X  0  X  X  X  0  0  0  0  0  X  X  X  0  X  X  X  0  0  0  0  X  0  X  X  0  X  0  X  X  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  0  X  X  X  X  0  0  X  X  0  0  0  0  X  X  0  0  X  X  0  X  X  0  0  0

generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+7x^88+12x^89+7x^90+4x^93+1x^98

The gray image is a linear code over GF(2) with n=174, k=5 and d=88.
As d=88 is an upper bound for linear (174,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.122 seconds.