The generator matrix

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

generates a code of length 87 over Z2[X]/(X^2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+27x^86+64x^87+28x^88+4x^94+3x^96+1x^118

The gray image is a linear code over GF(2) with n=174, k=7 and d=86.
As d=86 is an upper bound for linear (174,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.168 seconds.