The Code Aperture Snapshot Spectral Imaging system (CASSI) senses the spectral information of a scene using the underlying concepts of compressive sensing (CS). The random projections in CASSI are localized such that each measurement contains spectral information only from a small spatial region of the data cube. The goal of this paper is to translate high-resolution hyperspectral scenes into compressed signals measured by a low-resolution detector. Spatial super-resolution is attained as an inverse problem from a set of low-resolution coded measurements. The proposed system not only offers significant savings in size, weight and power, but also in cost as low resolution detectors can be used. The proposed system can be efficiently exploited in the IR region where the cost of detectors increases rapidly with resolution. The simulations of the proposed system show an improvement of up to 4 dB in PSNR. Results also show that the PSNR of the reconstructed data cubes approach the PSNR of the reconstructed data cubes attained with high-resolution detectors, at the cost of using additional measurements.