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

generates a code of length 74 over Z2[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+8x^78+7x^80

The gray image is a linear code over GF(2) with n=148, k=4 and d=78.
As d=78 is an upper bound for linear (148,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.0655 seconds.