Two-tower models are a prevalent matching framework for recommendation, which have been widely deployed in industrial applications. The success of two-tower matching attributes to its efficiency in retrieval among a large number of items, since the item tower can be precomputed and used for fast Approximate Nearest Neighbor (ANN) search. However, it suffers two main challenges, including limited feature interaction capability and reduced accuracy in online serving. Existing approaches attempt to design novel late interactions instead of dot products, but they still fail to support complex feature interactions or lose retrieval efficiency. To address these challenges, we propose a new matching paradigm named SparCode, which supports not only sophisticated feature interactions but also efficient retrieval. Specifically, SparCode introduces an all-to-all interaction module to model fine-grained query-item interactions. Besides, we design a discrete code-based sparse inverted index jointly trained with the model to achieve effective and efficient model inference. Extensive experiments have been conducted on open benchmark datasets to demonstrate the superiority of our framework. The results show that SparCode significantly improves the accuracy of candidate item matching while retaining the same level of retrieval efficiency with two-tower models.