  The confinement of ultracold neutrons (UCNs) in a three dimensional magnetic
field gradient trap allows for a measurement of the free neutron lifetime with
superior control over spurious loss channels and can provide a large kinetic
energy acceptance to enhance statistical sensitivity. In this paper, we present
the first successful implementation of a pulsed spin-flip based loading scheme
for a three-dimensional magnetic UCN trap. The measurements with the
$\tau$SPECT experiment were performed at the pulsed UCN source of the research
reactor TRIGA Mainz. We report on detailed investigations of major systematic
effects influencing the neutron storage time, statistically limited by the size
of the recorded data set. The extracted neutron storage time constant of $\tau
= 859(16)\mathrm{s}$ is compatible with, but not to be interpreted as, a
measurement of the free neutron lifetime.
