The efficacy of data decoding in contemporary ultrafast fiber transmission systems is greatly determined by the capabilities of the signal processing tools that are used. The received signal must not exceed a certain level of complexity, beyond which the applied signal processing solutions become insufficient or slow. Moreover, the required signal-to-noise ratio of the received signal can be challenging, especially when adopting modulation formats with multi-level encoding. Lately, photonic reservoir computing (RC) - a hardware machine learning technique with recurrent connectivity - has been proposed as a post-processing tool that deals with deterministic distortions from fiber transmission. Here we show that RC post-processing is remarkably efficient for multilevel encoding and for the use of very high launched optical peak power for fiber transmission up to 14dBm. Higher power levels provide the desired high signal-to-noise ratio (SNR) values at the receiver end, at the expense of a complex nonlinear transformation of the transmission signal. Our demonstration evaluates a direct fiber communication link with 4-level pulse amplitude modulation (PAM-4) encoding and direct detection, without including optical amplification, dispersion compensation, pulse shaping or other digital signal processing (DSP) techniques. By applying RC post-processing on the distorted signal, we numerically estimate fiber transmission distances of 27km at 56Gb/s and of 5.5 km at 112Gb/s data encoding rates, while fulfilling the hard-decision forward error correction (HD-FEC) bit-error-rate (BER) limit for data recovery. In an experimental equivalent demonstration of our photonic reservoir, the achieved distances are 21km and 4.6km respectively.