The generator matrix

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

generates a code of length 77 over Z2[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+4x^81+6x^82+4x^83+1x^84

The gray image is a linear code over GF(2) with n=154, k=4 and d=81.
As d=81 is an upper bound for linear (154,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.0736 seconds.