In architectural interior design, miscommunication frequently arises as clients lack design knowledge, while designers struggle to explain complex spatial relationships, leading to delayed timelines and financial losses. Recent advancements in generative layout tools narrow the gap by automating 3D visualizations. However, prevailing methodologies exhibit limitations: rule-based systems implement hard-coded spatial constraints that restrict participatory engagement, while data-driven models rely on extensive training datasets. Recent large language models (LLMs) bridge this gap by enabling intuitive reasoning about spatial relationships through natural language. This research presents an LLM-based, multimodal, multi-agent framework that dynamically converts natural language descriptions and imagery into 3D designs. Specialized agents (Reference, Spatial, Interactive, Grader), operating via prompt guidelines, collaboratively address core challenges: the agent system enables real-time user interaction for iterative spatial refinement, while Retrieval-Augmented Generation (RAG) reduces data dependency without requiring task-specific model training. This framework accurately interprets spatial intent and generates optimized 3D indoor design, improving productivity, and encouraging nondesigner participation. Evaluations across diverse floor plans and user questionnaires demonstrate effectiveness. An independent LLM evaluator consistently rated participatory layouts higher in user intent alignment, aesthetic coherence, functionality, and circulation. Questionnaire results indicated 77% satisfaction and a clear preference over traditional design software. These findings suggest the framework enhances user-centric communication and fosters more inclusive, effective, and resilient design processes. Project page: https://rsigktyper.github.io/AICodesign/