I built a circuit in Qiskit with two GHZ states. In the beginning, I created the superposition $\sim\bigg(|0000\rangle+|0101\rangle+|1010\rangle+|1111\rangle\bigg)$ with two $H$s, and two $CNOT$s.

Now, I want to amplify the result $|1111\rangle$ to over $50\%$. The maximum I got was around $40\%$, and for this case, I calculated that I needed only one iteration. I also tried more, but with no success.

Edit: Can anyone tell me how to implement Amplitude Amplification without needing to apply state initialization operator and the inverse of it because the state initialization operator could be highly complex?