Base stations in 5G and beyond use advanced antenna systems (AASs), where multiple passive antenna elements and radio units are integrated into a single box. A critical bottleneck of such a system is the digital fronthaul between the AAS and baseband unit (BBU), which has limited capacity. In this paper, we study an AAS used for precoded downlink transmission over a multi-user multiple-input multiple-output (MU-MIMO) channel. First, we present the baseline quantization-unaware precoding scheme created when a precoder is computed at the BBU and then quantized to be sent over the fronthaul. We propose a new precoding design that is aware of the fronthaul quantization. We formulate an optimization problem to minimize the mean squared error at the receiver side. We rewrite the problem to utilize mixed-integer programming to solve it. The numerical results manifest that our proposed precoding greatly outperforms quantization-unaware precoding in terms of sum rate.