For matrix $A = \begin{bmatrix} 0 & 4 & -1 & 1\\-2 & 6 & -1 & 1\\-2 & 8 & -1 & -1\\-2 & 8 & -3 & 1 \end{bmatrix}$, the characteristic polynomial of $A$ is $\charpoly{A}{x} = (x+2)(x-2)^2(x-4)$. Find the eigenvalues and corresponding eigenspaces of $A$.