What if generalised eigenvector is the zero vector

Question

I have a 3*3 matrix A= $$\begin{pmatrix} 3 & 0 & -1 \\ -1 & 2 & 1 \\ 1 & 2 & 3 \\ \end{pmatrix}$$ that has two eigenvalues $\lambda_1$=$\lambda_2$=2 and $\lambda_3$=4 so the eigenvalue which equals 2 has algebraic multiplicity two. However the eigenvector which equals 2 only has one vector which spans its eigenspace and therefore has geometric multiplicity 1. As usual there is one vector spanning the eigenspace corresponding to eigenvalue 4. However when I look for generalised eigenvectors corresponding to eigenvalue 2 by working out ker((A-2I)^2), only the zero vector is contained in it. How do I find a basis of eigenvectors and generalised eigenvecotrs of the matrix A if the only generalised eigenvector is the zero vector, which by definition is not allowed?