Suppose, $L$ is context-free language. Now, Pumping lemma for CFL says:
$\exists n$ such that $\forall z \in L$ with $|z| \geq n,$
$\exists z$ such that $z=uvtxy$ with
- $|vtx| \leq n$
- $|vx| >0$
- $\forall i \geq 0, uv^itx^iy \in L$
Now, consider an element of set $L$ as $z= aba^nbab^n$
Here, $z \in L$ and $|z| \geq n$
Now, try to decompose $z$ as $z=uvtxy = aba a^2a^{n-3}bab^n$ with
$u = aba, v = a^2, t = a^{n-3},x=b,y=ab^n$
Here, we can see $|vtx| \leq n$ and $|vx| >0$
Now, pump this string two times i.e. for $i=2, uv^itx^iy$ is:
$uv^2tx^2y = abaa^4a^{n-3}b^2ab^n = aba^{n-2}b^2ab^n$ which is not in $L$ but according to pumping lemma, it should be in $L.$ So, Contradiction. So, what we have assumed is incorrect and hence, $L$ is not a context-free language.