Optical quantum memories are essential components for realizing the full potential of quantum networks. Among these, rare-earth-doped crystal memories stand out due to their large multimode storage capabilities. To maximize the multimode capacity in the time domain, it is key to simultaneously achieve large memory bandwidth and long optical storage time. Here, we demonstrate an atomic frequency comb optical memory in ¹⁷¹Yb³⁺:Y₂SiO₅ , with a memory bandwidth of 250 MHz and a storage time of up to 125 µs. The efficiency reaches 20% at short storage times, and 5% at 125 µs. These results were enabled by an optimized optical pumping scheme, guided by numerical modelling. Our approach is specifically designed for future spin-wave storage experiments, with the theoretical bandwidth limit set at 288 MHz by the hyperfine structure of ¹⁷¹Yb³⁺:Y₂SiO₅ . Additionally, we introduce an efficient method for synthesizing the optical pumping waveforms required for generating combs with tens of thousands of teeth, as well as a simple yet frequency-agile laser setup for optical pumping across a 10 GHz bandwidth.