Quantum Random Number Generators (QRNGs) serve as high-entropy sources for Quantum Key Distribution (QKD) systems. However, the raw data from these quantum sources require post-processing to achieve a nearly uniform distribution. This work presents a state-of-the-art implementation of the Toeplitz Strong Extractor on an FPGA, achieving a benchmark extraction speed of 26.57 Gbps. A detailed implementation flow of the post-processing on the FPGA is provided, along with the execution speeds obtained for different randomness extraction ratios. Raw data from an in-house phase noise-based QRNG is processed on the FPGA using this implementation, and the output is validated using the NIST STS 2.1.2 statistical randomness test suite.