  We present a systematic search for transiting giant planets ($0.6 R_{\rm J}
\leq R_{\rm P} \leq 2.0 R_{\rm J}$) orbiting nearby low-mass stars ($M_{*} \leq
0.71 M_{\odot}$). The formation of giant planets around low-mass stars is
predicted to be rare by the core-accretion planet formation theory. We search
91,306 low-mass stars in the TESS 30 minute cadence photometry detecting
fifteen giant planet candidates, including seven new planet candidates which
were not known planets or identified as TOIs prior to our search. Our
candidates present an exciting opportunity to improve our knowledge of the
giant planet population around the lowest mass stars. We perform planet
injection-recovery simulations and find that our pipeline has a high detection
efficiency across the majority of our targeted parameter space. We measure the
occurrence rates of giant planets with host stars in different stellar mass
ranges spanning our full sample. We find occurrence rates of $0.137 \pm 0.097$%
(0.088 - 0.26 $M_{\odot}$), $0.108 \pm 0.083$% (0.26 - 0.42 $M_{\odot}$), and
$0.29 \pm 0.15$% (0.42 - 0.71 $M_{\odot}$). For our full sample (0.088 - 0.71
$M_{\odot}$) we find a giant planet occurrence rate of $0.194 \pm 0.072$%. We
have measured for the first time the occurrence rate for giant planets orbiting
stars with $M_{*} \leq 0.4 M_{\odot}$ and we demonstrate this occurrence rate
to be non-zero. This result contradicts currently accepted planet formation
models and we discuss some possibilities for how these planets could have
formed.
