Ideation is a critical component of video-based design (VBD), where videos serve as the primary medium for design exploration and inspiration. The emergence of generative AI offers considerable potential to enhance this process by streamlining video analysis and facilitating idea generation. In this paper, we present DesignMinds, a prototype that integrates a state-of-the-art Vision-Language Model (VLM) with a context-enhanced Large Language Model (LLM) to support ideation in VBD. To evaluate DesignMinds, we conducted a between-subject study with 35 design practitioners, comparing its performance to a baseline condition. Our results demonstrate that DesignMinds significantly enhances the flexibility and originality of ideation, while also increasing task engagement. Importantly, the introduction of this technology did not negatively impact user experience, technology acceptance, or usability.