This paper introduces Non-Orthogonal OTFS-IMMA (NOTFS-IMMA), an enhanced uplink random access scheme that integrates Non-Orthogonal Multiple Access (NOMA) with Orthogonal Time Frequency Space (OTFS) and Index Modulation Multiple Access (IMMA). In OTFS-IMMA, users randomly select delay-Doppler resource blocks (DDRBs) based on portions of their data, enabling grant-free access without coordination, thus improving energy efficiency. Analytical and simulation results demonstrate that NOTFS-IMMA outperforms both traditional OTFS multiple access and OTFS-IMMA in terms of bit error rate (BER) and spectral efficiency.