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

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+8x^81+3x^82+3x^84+1x^86

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 0.076 seconds.