The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+32x^89+12x^90+12x^92+4x^94+3x^96

The gray image is a linear code over GF(2) with n=178, k=6 and d=89.
As d=89 is an upper bound for linear (178,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.134 seconds.