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

generates a code of length 79 over Z2[X]/(X^2) who�s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+14x^84+1x^88

The gray image is a linear code over GF(2) with n=158, k=4 and d=84.
As d=84 is an upper bound for linear (158,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.0838 seconds.