Materials suitable for magnonic crystals demand low magnetic damping and long spin-wave propagation distance. In this context Co-based Heusler compounds are ideal candidates for magnonic based applications. In this work, antidot arrays (with different shapes) of epitaxial Co2Fe0.4Mn0.6Si Heusler-alloy thin films are prepared using e-beam lithography and sputtering technique. Magneto-optic Kerr effect (MOKE) and ferromagnetic resonance analysis confirm the presence of dominant cubic and moderate uniaxial magnetic anisotropies in the thin film. Domain imaging via x-ray photoemission electron microscopy on the antidot arrays reveals chainlike switching or correlated bigger domains for different antidot shapes. Time-resolved MOKE microscopy is performed to study the precessional dynamics and magnonic modes of the antidots with different shapes. We show that the optically induced spin-wave spectra in such antidot arrays can be tuned by changing the shape of the holes. The variation in internal-field profiles, pinning energy barrier, and anisotropy modifies the spin-wave spectra dramatically within the antidot arrays with different shapes. We further show that by combining the magnetocrystalline anisotropy with the shape anisotropy, an extra degree of freedom can be achieved to control the magnonic modes in such antidot lattices.