The need to limit climate change has led to policies that aim for the reduction of greenhouse gas emissions. Often, a trade-off exists between reducing emissions and associated costs. In this article, a multi-objective optimization framework is proposed to determine this trade-off when operating a Community Energy Storage (CES) system in a neighbourhood with high shares of photovoltaic (PV) electricity generation capacity. The Pareto frontier of costs and emissions objectives is established when the CES system would operate on the day-Ahead spot market. The emission profile is constructed based on the marginal emissions. Results show that costs and emissions can simultaneously be decreased for a range of solutions compared to reference scenarios with no battery or a battery only focused on increasing self-consumption, for very attractive CO2 abatement costs and without hampering self-consumption of PV-generated electricity. Results are robust for battery degradation, whereas battery efficiency is found to be an important determining factor for simultaneously decreasing costs and emissions. The operational schedules are tested against violating transformer, line and voltage limits through a load flow analysis. The proposed framework can be extended to employ a wide range of objectives and/or location-specific circumstances.