The authentication of printed documents is an important problem these days. Numerous authentication techniques have been proposed in the relevant literature. One of the most promising solutions uses copy-sensitive graphical codes made of particular patterns. The two Level QR (2LQR) code uses specific textured patterns in order to ensure the sensitivity to duplication process. The authentication test of this code is based on comparing the correlation values between the original and the printed-and-scanned codes with a predetermined threshold. The weakest feature of this technique is the rejection of authentic codes due to the small gap between correlation values for authentic and duplicated code. In this paper, we propose to reduce the number of false-negative results of the authentication test by using a very competitive Super-Resolution (SR) technique. The experimental results show the significant improvement of correlation values when using the images printed-and-scanned once, without increasing the correlation values of duplicated codes. Therefore, the 2LQR code copy sensitivity is not affected by the suggested quality improvement process.