Reservoir computing is an analog bio-inspired computation scheme for efficiently processing time-dependent signals, the photonic implementations of which promise a combination of massive parallel information processing, low power consumption, and high-speed operation. However, most of these implementations, especially for the case of time-delay reservoir computing, require extensive multi-dimensional parameter optimization to find the optimal combination of parameters for a given task. We propose a novel, largely passive integrated photonic TDRC scheme based on an asymmetric Mach-Zehnder interferometer in a self-feedback configuration, where the nonlinearity is provided by the photodetector, and with only one tunable parameter in the form of a phase shifting element that, as a result of our configuration, allows also to tune the feedback strength, consequently tuning the memory capacity in a lossless manner. Through numerical simulations, we show that the proposed scheme achieves good performance -when compared to other integrated photonic architectures- on the temporal bitwise XOR task and various time series prediction tasks, while greatly reducing hardware and operational complexity.