The generator matrix

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

generates a code of length 77 over Z2[X]/(X^2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+32x^77+15x^78+15x^80+1x^94

The gray image is a linear code over GF(2) with n=154, k=6 and d=77.
As d=77 is an upper bound for linear (154,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.193 seconds.