So that, strictly speaking, you have NOT yet solved the problem. The "null space" is a one-dimensional subspace of $\displaystyle R^4$ and you have found one vector in that space. How would you represent any vector in the null space?
Yes, or, to phrase it slightly differently, $\displaystyle t\begin{bmatrix}0 \\ 0 \\ -2 \\ 1\end{bmatrix}$, the set of all real multiples of your original vector= the subspace spanned by that vector.