  We introduce a spinful variant of the complex Sachdev-Ye-Kitaev model with
time reversal symmetry, which can be solved exactly in the limit of a large
number $N$ of degrees of freedom. At low temperature, the phase diagram of the
model includes a compressible non-Fermi liquid and a strongly-correlated spin
singlet superconductor that shows a tunable enhancement of the gap ratio
predicted by BCS theory. The two phases are separated by a first-order phase
transition, in the vicinity of which a gapless superconducting phase is
stabilized. We also discuss time-reversal breaking perturbations that introduce
a finite magnetization coexisting with superconductivity.
