We present a novel approach to text detection for document images. For robust text detection of noisy scanned or captured document images, the advantages of multi-task learning are adopted by adding an auxiliary task of text enhancement. Consequently, our proposed model trains reducing noise and enhancing text regions as well as detecting text. To overcome the insufficiency of document image data for text detection, train data for our model are enriched with synthesized document images that are fully labeled for text detection and enhancement. For the effective use of synthetic and real data, the proposed model is trained in two phases. The first phase is training only synthetic data in a fully-supervised manner. Then real data with only detection labels are added in the second phase. The enhancement task for real data is weakly-supervised with information from detection labels. Our methods are demonstrated on a real document dataset with performances exceeding those of other methods. Also, we conducted ablations to analyze effects of the synthetic data, multi-task, and weak-supervision. Whereas the existing text detection studies mostly focus on the text in scenes, our proposed method is optimized to the applications for the text in scanned or captured documents.