Based on equations of motion of an SO(5) pseudo-spin, we demonstrate a quantum quench protocol using the magnetic pulse to excite an $\textit{undamped}$ heavy Higgs boson in the Balian--Werthamer superfluid (or superconductor). To achieve that, it is essential to include the dipolar interaction in the effective Hamiltonian and to calculate the ground state self-consistently. The pumped heavy Higgs mode has the twisted angular momentum $J=2$ with the projection $J^{\,}_z=0$ and couples to a well-known light Higgs mode ($J=1$, $J^{\,}_z=0$). The numerical method of 26-point Lebedev quadrature is implemented concretely so as to observe the real-time coupled oscillation.