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

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

Homogenous weight enumerator: w(x)=1x^0+50x^88+8x^92+4x^96+1x^112

The gray image is a linear code over GF(2) with n=176, k=6 and d=88.
As d=88 is an upper bound for linear (176,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.167 seconds.