The generator matrix

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

generates a code of length 38 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+13x^40+2x^44

The gray image is a linear code over GF(2) with n=76, k=4 and d=40.
As d=40 is an upper bound for linear (76,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.0082 seconds.