I'm hoping someone can help me out with finding an example of the following:

a nontrivial fiber bundle $Y \hookrightarrow Z \rightarrow X$ where $X,Y,$ and $Z$ are all compact even dimensional spin manifolds with first Pontryagin classes satisfying $p_1(Z)=0$ and $p_1(X)\neq 0$. I'd also like dim $Y\geq8$.

Thanks in advance.