LLM-based RTL code generation methods increasingly target both functional correctness and PPA quality, yet existing approaches decouple the two objectives, optimizing PPA only after full correctness is achieved. Sequential multi-agent pipelines, evolutionary search with binary correctness gates, and hierarchical reward dependencies all discard partially correct but architecturally promising candidates. Moreover, existing methods reduce the multi-objective PPA space to a single scalar fitness that obscures 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 with fine-grained scoring. The framework allows PPA-promising but partially correct candidates to guide the search toward jointly optimal solutions, and further employs four-dimensional Pareto-based non-dominated sorting to preserve the PPA trade-off structure without manual weight tuning. On VerilogEval 2.0 and RTLLM 2.0, COEVO surpasses all agentic baselines across four LLM backbones. With GPT-5.4-mini, COEVO achieves 97.5\% and 94.5\% Pass@1 and attains the best PPA on 43 out of 49 synthesizable RTLLM 2.0 designs.

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