LLM-based RTL code generation methods increasingly target both functional correctness and PPA quality, yet existing approaches universally decouple the two objectives, optimizing PPA only after correctness is fully achieved. Whether through sequential multi-agent pipelines, evolutionary search with binary correctness gates, or hierarchical reward dependencies, partially correct but architecturally promising candidates are systematically discarded. Moreover, existing methods reduce the multi-objective PPA space to a single scalar fitness, obscuring the trade-offs among area, delay, and power. To address these limitations, we propose COEVO, a co-evolutionary framework that unifies correctness and PPA optimization within a single evolutionary loop. COEVO formulates correctness as a continuous co-optimization dimension alongside area, delay, and power, enabled by an enhanced testbench that provides fine-grained scoring and detailed diagnostic feedback. An adaptive correctness gate with annealing allows PPA-promising but partially correct candidates to guide the search toward jointly optimal solutions. To preserve the full PPA trade-off structure, COEVO employs four-dimensional Pareto-based non-dominated sorting with configurable intra-level sorting, replacing scalar fitness without manual weight tuning. Evaluated on VerilogEval 2.0 and RTLLM 2.0, COEVO achieves 97.5\% and 94.5\% Pass@1 with GPT-5.4-mini, surpassing all agentic baselines across four LLM backbones, while attaining the best PPA on 43 out of 49 synthesizable RTLLM designs.