Biologically Inspired Design (BID), or Biomimicry, is a problem-solving methodology that applies analogies from nature to solve engineering challenges. For example, Speedo engineers designed swimsuits based on shark skin. Finding relevant biological solutions for real-world problems poses significant challenges, both due to the limited biological knowledge engineers and designers typically possess and to the limited BID resources. Existing BID datasets are hand-curated and small, and scaling them up requires costly human annotations. In this paper, we introduce BARCODE (Biological Analogy Retriever), a search engine for automatically mining bio-inspirations from the web at scale. Using advances in natural language understanding and data programming, BARCODE identifies potential inspirations for engineering challenges. Our experiments demonstrate that BARCODE can retrieve inspirations that are valuable to engineers and designers tackling real-world problems, as well as recover famous historical BID examples. We release data and code; we view BARCODE as a step towards addressing the challenges that have historically hindered the practical application of BID to engineering innovation.