Pumping lemma for an involved non context free language

Hi I’m trying to show $C={wzzw^R|w,zin{0,1}^+}$ is not a context-free language.( I have this believe because $C={ww|win{0,1}^+}$ is not a context free language.) I’m really struggling to come up with a string that captures the essence of irregularity of this language: I tried strings like $s=1^p0^p1^p0^p1^p1^p$ but there are too many cases to deal with and most of the examples I saw only use 1 or 2 cases, so I believe the direction I’m going is wrong. Can you provide a hint on which string to pick as the ‘pumping string’? Thank you.