Background and Context: Peer code review activities provide well-documented benefits to students in programming courses. Students develop relevant skills through exposure to alternative coding solutions, producing and receiving feedback, and collaboration with peers. Despite these benefits, low student motivation has been identified as one of the challenges leading to poor engagement and substandard review quality. Objective: This research investigates gamification as a technique for motivating students to generate high-quality reviews. Method: We conduct a randomised controlled study, explore the nature and length of the feedback produced by students, and measure how students perceive the value of the feedback they receive and produce. We manually categorise students' feedback into several categories adapted from a published taxonomy for student peer review. This categorisation indicates whether the feedback contains actionable advice and identifies strengths and weaknesses in the code. Findings: We found that the quality of the feedback differed significantly between experimental and control conditions. Students in the experimental condition wrote longer comments and tended to produce more specific advice for their peers. Implications: The findings can assist educators in understanding how the chosen game mechanics can be a potential strategy to motivate students to produce high-quality written feedback in peer code review activities.