The generator matrix

 1  0  1  1  1  0  1  1  X  1  1  X  1  1  0  1  1  0  1  1  X  1  1  X  1  1  0  1  1  0  1  1  1  1  X  X  X  X  0  0  1  1  0  1  1  X  1  1  1  1  0  X  1  1  1  1  X  X  0  X  X  0  0  1  1  1  1  0  X  0  X  X  X  0  X  X  0  0  1  1
 0  1  1  0 X+1  1  X X+1  1  X  1  1  0 X+1  1  0 X+1  1  X  1  1  X  1  1  0 X+1  1  0 X+1  1  X  X  1  1  1  1  0  X  X  0  0 X+1  1  X  1  1  0  X X+1  1  1  1  0  X  0  X  0  X  X  0  X  X  0 X+1  1 X+1  1  1  1  1  1  0  X  X  0  X  X  0  0 X+1
 0  0  X  X  0  X  X  X  X  0  0  0  0  0  X  X  X  0  X  X  X  0  0  0  0  0  X  X  X  0  X  0  X  0  X  0  X  X  X  X  0  0  X  0  0  X  X  X  X  X  0  0  0  0  X  X  0  0  0  X  X  X  X  0  0  X  X  0  0  X  X  0  0  0  X  X  X  X  0  0

generates a code of length 80 over Z2[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+8x^81+10x^82+8x^83+2x^84+2x^86+1x^88

The gray image is a linear code over GF(2) with n=160, k=5 and d=81.
As d=81 is an upper bound for linear (160,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.11 seconds.