Evolution of the long-wavelength edge of supercontinuum (SC) in a large mode-area photonic crystal fiber (LMA PCF) under extreme (close to the fiber damage threshold) picosecond excitation is analyzed for the first time to our knowledge. The obtained results are interpreted on the basis of the numerical simulations explaining both spectral and temporal characteristics of SC in dependence on the pulse power and the fiber length. An existence of the minimum LMA PCF length providing the broadest spectrum under the highest picosecond excitations is predicted. The multimode cross-modulation inside the LMA PCF is analyzed, as well.