Data-intensive application tasks have always fueled research and development towards more powerful computing systems. In this context, the recently proposed framework of hyper-dimensional computing (HDC) is rapidly emerging to open new opportunities for the development of systems that perform cognitive tasks in hardware. The highly memory-centric nature of HDC was the key motivation for the in-memory computing hardware implementation approaches explored recently where memristive devices were used to locally implement logic operations. In this work, we explore using memristive devices to implement one of the fundamental modules of an HDC system, the "associative memory" (AM). We designed and simulated an HDC system in MATLAB software using a behavioral model for memristive devices and explored the performance of the HDC system in image classification tasks, using different AM implementations to enrich the representation of the image classes in the AM when they included up to 25% of noise. The simulation results also explored the impact of nonidealities of memristive devices and demonstrate the critical system design aspects to consider in such an implementation approach.