Pumping Lemma for CFL - $ \{ 0^{i} 1^{j} 0^{k} 1^{l} \hspace{0.2cm}| \hspace{0.2cm} i = l \hspace{0.2cm} \land j = k \} $
$\{ww\mid w\in\{0,1\}^*\}$ not being context-free does not imply every subset is also not context-free. In this case, $0^n1^n0^n1^n$ passes the pumping lemma, since it can be written as follows $0^p1^p0^p1^p=0^p1^{p-1}1^n0^n0^{p-1}1^p$.