Present orthogonal time frequency space modulation with index modulation (OTFS-IM) techniques activate a given number of grids in the delay-Doppler (DD) domain and employ fixed constellation as changing them would result in ambiguous detection. Motivated by this, we propose a novel enhanced OTFS with index modulation (E-OTFS-IM) scheme which permits changing the number of active grids conveying modulation symbols from any constellation. The proposed E-OTFS-IM scheme alleviates ambiguous detection by jointly mapping information to grid activation pattern in DD domain and 2D modulation symbols. We also propose an efficient encoding method for E-OTFS-IM. In addition, an updated message passing (MP) detection suitable for E-OTFS-IM as well as its low-complexity improvement are developed. We derive a average bit error probability (ABEP) upper bound for our proposed E-OTFS-IM scheme employing the maximum likelihood detector. Additionally, we also propose an enhanced scheme named E-OTFS-IM with in-phase/quadrature (E-OTFS-IM-IQ) to further improve the spectral efficiency and reliability. In E-OTFS-IM-IQ, the principle of E-OTFS-IM is extended to in-phase and quadrature branches independently. The efficient encoding method and MP detector for this modified scheme is also introduced. Simulation results confirm that the derived ABEP upper bound is tight in the high signal-to-noise ratio region, and show that our proposed E-OTFS-IM improves the performance of conventional OTFS and OTFS-IM. The results also indicate the proposed E-OTFS-IM-IQ achieves better bit error rate performance than E-OTFS-IM.