We investigate the enhanced terahertz generation in the organic crystal BNA when pumped by compressed high-energy ytterbium laser pulses. By compressing the pump pulses from 170 fs down to 43 fs using an argon-filled hollow-core fiber and chirped mirrors, the terahertz conversion efficiency is increased by 2.4 times, leading to the generation of multi-microjoule terahertz pulses with a frequency spectrum almost twice as wide, extending up to 19 THz. These findings showcase a simple and efficient way to generate intense and broadband terahertz pulses by means of an amplified ytterbium laser system.