Matched filtering of quadriphase coded radar signals creates unwanted sidelobes, which may mask important information. This correspondence presents a method of eliminating these sidelobes in aperiodic quadriphase codes. This is done by using a mismatched filter. The signal-to-noise ratio (SNR) at the output of the mismatched filter is less than the SNR at the output of the corresponding matched filter. A thorough computer search has been carried out to find quadriphase code-mismatched filter pairs with minimum possible SNR losses by considering a point target in the presence of white Gaussian noise. The phase patterns of the optimal codes, which were chosen from a total number of 1.466 times 1012investigated codes, are shown. It turned out that the mismatched filter of a quadriphase Barker code with 15 elements (1, 1, 1,j,j, 1, -j, -j,j, -1, -j,j, 1, -1, 1) has a loss in SNR of only 6.7% when compared with the corresponding matched filter. The mismatched filter of the well known 13-element Barker code, which has a loss in SNR of 4.8%, outperforms this filter. Finally, using numerical experiment it is shown that a randomly selected long code will most likely have very large SNR losses.