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

generates a code of length 89 over Z2[X]/(X^2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+28x^88+64x^89+28x^90+3x^96+3x^98+1x^130

The gray image is a linear code over GF(2) with n=178, k=7 and d=88.
As d=88 is an upper bound for linear (178,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.137 seconds.