  We examine the appearance of superconductivity in the strong-coupling limit
of the Hubbard model on the pyrochlore lattice. We focus upon the limit of half
filling, where the normal-state band structure realizes a $j=3/2$ semimetal.
Introducing doping, we show that the pairing is favored in a $J=2$ quintet
$E_g$ state. The attractive interaction in this channel relies on the fact that
$E_g$ pairing on the pyrochlore lattice avoids the detrimental on-site
repulsion. Our calculations show that a time-reversal symmetry-breaking
superconducting phase is favored, which displays Bogoliubov Fermi surfaces.
