Construction a club $C\subseteq\omega_1$ and a scale of length $\aleph_{\omega_1+1}$ in $\prod_{\alpha \in C}\aleph_{\alpha+1}/J$

Question

I want to construct a club $C\subseteq\omega_1$ and a scale of length $\aleph_{\omega_1+1}$ in $\prod_{\alpha \in C}\aleph_{\alpha+1}/J$

When $J$ is the ideal of bounded sets

I tried to use the club of all the limit ordinal in $\omega_1$ and construct the scale recursively, but I do not know how to build it so that it will be unbounded in $\omega_1$.