While quantum computers are rapidly becoming more powerful, the current cryptographic infrastructure is imminently threatened. In a preventive manner, the U.S. National Institute of Standards and Technology (NIST) has initiated a process to evaluate quantum-resistant cryptosystems, to form the first post-quantum (PQ) cryptographic standard. Classic McEliece (CM) is one of the most prominent cryptosystems considered for standardization in NIST's PQ cryptography contest. However, its computational cost poses notable challenges to a big fraction of existing computing devices. This work presents an HLS-based, HW/SW co-design acceleration of the CM Key Encapsulation Mechanism (CM KEM). We demonstrate significant maximum speedups of up to 55.2×, 3.3×, and 8.7× in the CM KEM algorithms of key generation, encapsulation, and decapsulation respectively, comparing to a SW-only scalar implementation.This paper has the following structure: Section II introduces the CM cryptosystem and presents the motivation for this work. Section III analyzes our HW/SW co-design proposal. Next, Section IV explains our experimental methodology.