In this work, we consider reliable transmissions for grant-free random access (GFRA) when machine-type communication (MTC) devices have a message of multiple short data packets to transmit. An existing approach is based on <inline-formula> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula>-repetition for reliable transmissions. In order to improve the reliability, a random network coding based scheme is proposed, where each device in GFRA employs random network coding to transmit packets that are linear combinations of its original packets. To shed light on the performance behaviors of the conventional <inline-formula> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula>-repetition and proposed schemes, we derive their error probabilities and provide an indicative analysis. Simulation results validate our derivations and show that the proposed scheme by exploiting random network coding can perform significantly better than conventional <inline-formula> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula>-repetition one.