Plane-wave ultrasound image reconstruction based on Fourier-domain beamforming is known to be highly efficient, but it needs to access individual frames of raw channel data all at once. To reduce data storage and transfer costs, we propose to quantize channel data samples using a small codebook, whose dynamically scaled entries are then used during reconstruction. Based on publicly available experimental data, we show that it is possible to obtain good-quality images with a 16-entry codebook, i.e., only 4 bits per sample are needed.