In the research of next-generation wireless communication technologies, orthogonal time frequency space (OTFS) modulation is emerging as a promising technique for high-speed mobile environments due to its superior efficiency and robustness in doubly selective channels. Additionally, the cell-free architecture, which eliminates the issues associated with cell boundaries, offers broader coverage for radio access networks. By combining cell-free network architecture with OTFS modulation, the system may meet the demands of massive random access required by machine-type communication devices in high-speed scenarios. This paper explores a massive random access scheme based on OTFS modulation within a cell-free architecture. A transceiver model for uplink OTFS signals involving multiple access points (APs) is developed, where channel estimation with fractional channel parameters is approximated as a block sparse matrix recovery problem. Building on existing superimposed and embedded preamble schemes, a hybrid preamble scheme is proposed. This scheme leverages superimposed and embedded preambles to respectively achieve rough and accurate active user equipment (UEs) detection (AUD), as well as precise channel estimation, under the condition of supporting a large number of access UEs. Moreover, this study introduces a generalized approximate message passing and pattern coupling sparse Bayesian learning with Laplacian prior (GAMP-PCSBL-La) algorithm, which effectively captures block sparse features after discrete cosine transform (DCT), delivering precise estimation results with reduced computational complexity. Simulation results demonstrate that the proposed scheme is effective and provides superior performance compared to other existing schemes.