The Be-14 nucleus is investigated in the three-cluster generator coordinate method, involving several Be-12+n + n configurations. The Be-12 core nucleus is described in the harmonic oscillator model with all possible configurations in the p shell. We present the theoretical energy spectrum of Be-14 up to 5 MeV excitation energy, and show that the matter densities support a halo structure of the ground state. A strong enhancement of the rms radius with respect to the Be-12 core is obtained, in agreement with experiment. Our calculation indicates that the Be-12(g.s.)+n + n configuration represents 66% only of the total wave function, and that core excitations cannot be neglected. A comparative study of the Be-12, Be-13, and Be-14 nuclei is performed with identical conditions of calculation. We also analyze dipole and quadrupole excitations of the Be-14 ground state, and show that a significant part of the sum rules for soft modes is exhausted at low excitation energies.