With recent advancements in next-generation data storage, especially in biological molecule-based storage, insertion, deletion, and substitution (IDS) error-correcting codes have garnered increased attention. However, a universal method for designing tailored IDS-correcting codes across varying channel settings remains underexplored. We present an autoencoder-based approach, THEA-code, aimed at efficiently generating IDS-correcting codes for complex IDS channels. In the work, a disturbance-based discretization is proposed to discretize the features of the autoencoder, and a simulated differentiable IDS channel is developed as a differentiable alternative for IDS operations. These innovations facilitate the successful convergence of the autoencoder, producing channel-customized IDS-correcting codes that demonstrate commendable performance across complex IDS channels, particularly in realistic DNA-based storage channels.