Barcodes and 2D codes are widely used for various purposes, such as electronic payments and product management. Special code readers, and consumer smartphones can be used to scan codes; thus concerns about fraud and authenticity are important. Embedding watermarks in 2D codes, which allows simultaneous recognition and tamper detection by simply analyzing the captured pattern without requiring an additional device is considered a promising solution. However, smartphone cameras frequently suffer misfocus especially if the target object is too close to the lens, which makes the captured image defocused and results in failure to read watermarks. In this paper, we propose the use of a coded aperture imaging technique to recover watermarks. We have designed a coded aperture that is robust against defocus blur by optimizing the aperture pattern using a genetic algorithm. In addition, we have developed a programmable coded aperture that includes an actual optical process that works in an optimization loop; thus, the complicated effects of the optical aberrations can be considered. Experimental results demonstrate that the proposed method can extend the depth of field for watermark extraction to 3.1 times wider than that of a general circular aperture.