Neutron scattering experiments have been performed on the ternary rare-earth diborocarbide ${\mathrm{Ce}}^{11}{\mathrm{B}}_{2}{\mathrm{C}}_{2}$. The powder-diffraction experiment confirms formation of a long-range magnetic order at ${T}_{\mathrm{N}}=7.3\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, where a sinusoidally modulated structure is realized with the modulation vector $\mathbit{q}=[0.167(3),0.167(3),0.114(3)]$. Inelastic excitation spectra in the paramagnetic phase comprise significantly broad quasielastic and inelastic peaks centered at $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\approx}0$, 8, and $65\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. Crystalline-electric-field (CEF) analysis satisfactorily reproduces the observed spectra, confirming their CEF origin. The broadness of the quasielastic peak indicates strong spin fluctuations due to coupling between localized $4f$ spins and conduction electrons in the paramagnetic phase. A prominent feature is suppression of the quasielastic fluctuations, and concomitant growth of a sharp inelastic peak in a low-energy region below ${T}_{\mathrm{N}}$. This suggests dissociation of the conduction and localized $4f$ electrons on ordering, and contrasts the presently observed incommensurate phase with spin-density-wave order frequently seen in heavy fermion compounds, such as ${\mathrm{Ce}}_{x}{\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Ru}}_{2}{\mathrm{Si}}_{2}$.