In urban environments GNSS code multipath errors can cause large positioning errors. Many existing approaches try to overcome these errors employing Kalman innovations or statistical tests for code and carrier similarity. In this paper a new multipath model for time-differential code measurement errors is found from measurement data. The data indicates that the stochastic code error of multipath-affected time-differential pseudoranges follows a Laplacian distribution. A multipath detection algorithm is presented that exploits the new model. Our approach uses the likelihood functions of the white receiver noise and of the found Laplacian distribution to drive a hidden Markov model. It supposes two states - multipath-free and multipath-affected environment. In a simulation, realistic transition parameters of the Markov model were assumed and the detection rate of the proposed statistical test was determined. Compared to existing detection algorithms the false negative rate was reduced dramatically at a similar false positive rate. Due to the missing reference data for real-world measurements the performance has to be evaluated indirectly. A test drive was carried out and the horizontal positioning error was compared to a reference in a post-processing step. The error of epochs with at least one detection was significantly larger than the one when no measurements are detected as multipath-affected.