Inter-track interference (ITI) is a major source of signal impairment in the next-generation magnetic recording systems. The single-track read channel model, combined with anti-ITI signal detection schemes, is a popular way to recover single-track data from a readback signal corrupted by the ITI. On the other hand, the multi-track read channel model can be used to simultaneously recover multi-track data from a readback signal. However, the performance of multi-track detection is severely degraded by the weak signals from the sidetracks and the indistinguishable symbols. To improve this performance, in this paper we propose a two-dimensional coding in conjunction with an asymmetric iterative multi-track detection (A-IMD) scheme, which uses joint channel detection and decoding of two parallel six-symbol-based detectors concatenated with two parallel non-binary low-density parity-check (NB-LDPC) decoder over GF(4), to iteratively recover four-track data from two readback signals. Simulation results demonstrate that the performance of the multi-track detection can indeed be greatly improved by using the proposed A-IMD scheme.