The coded caching scheme proposed by Maddah- Ali and Niesen considers the delivery of items (files) in a given content library to users through the so-called single bottleneck link network. While the single bottleneck link network is a deterministic error-free model, where the multicast rate to all users is fixed irrespectively of the number of users, in order to apply this paradigm to a wireless network, it is important to make sure that the common rate at which the multicast message is transmitted remains large as the number of users increase. This paper focuses on a variant of the Maddah-Ali and Niesen scheme successively proposed for the so-called combination network, where the multicast message is further encoded by an MDS code and the MDS-coded blocks are simultaneously transmitted from different nodes, referred to in the wireless context of this paper as Remote Radio Heads (RRHs). In the proposed system, each user is equipped with an antenna array and can select to decode a certain number of RRH transmissions, while either zero-force some others, or simply treat the others (the weak ones) as noise. The system is "cell-free" in the sense that each user can independently and individually (in a usercentric manner) decide which RRHs to decode, without any explicit association of users to RRHs. We study the performance of the proposed system when users and RRHs are distributed according to 2-dimensional homogeneous Poisson Point Process ad the propagation is affected by Rayleigh fading and distance dependent pathloss. We use stochastic geometry to derive the average rate of a typical user and the ergodic rate CDF, where ergodicity is with respect to the small-scale Rayleigh fading and the randomness of the rates is due to the large-scale pathloss, which is random due to the random geometry. Our analysis allows to optimize the system with respect to the MDS coding rate. Also, form our analysis it follows that the proposed system is fully scalable, in the sense that it can support an arbitrarily large number of users, while maintaining a non-vanishing peruser rate.