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

generates a code of length 90 over Z2[X]/(X^2) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+28x^92+1x^96+2x^104

The gray image is a linear code over GF(2) with n=180, k=5 and d=92.
As d=92 is an upper bound for linear (180,5,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.166 seconds.