In a binary Transmitted Reference (TR) system each bit is encoded into two wavelets of finite duration. The information is transmitted by the sign of correlation measured between the two wavelets. The Code-Shifted Differential Chaos Shift Keying (CS-DCSK) modulation scheme transmits the two wavelets in the same time slot and applies two Walsh code sequences to keep the wavelets separated. The CS-DCSK modulation scheme is generalized here by transmitting more than one information bearing wavelets with one reference. The orthogonality of wavelets is assured by different Walsh code sequences. The new Generalized CS-DCSK (GCS-DCSK) scheme is a multilevel modulation where the symbol period is kept constant but the data rate can be varied in an adaptive manner by adding new or removing existing information bearing wavelets, each of them is isolated by Walsh code. Exploiting the Gaussian approximation, an analytical expression is derived for the noise performance of GCS-DCSK modulation. Its accuracy is verified by computer simulation.