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

generates a code of length 79 over Z2[X]/(X^2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+7x^80+16x^81+7x^82+1x^98

The gray image is a linear code over GF(2) with n=158, k=5 and d=80.
As d=80 is an upper bound for linear (158,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.0843 seconds.