  Heartbeat stars are eccentric binaries exhibiting characteristic shape of
brightness changes during periastron passage caused by tidal distortion of the
components. Variable tidal potential can drive tidally excited oscillations
(TEOs), which are usually gravity modes. Studies of heartbeat stars and TEOs
open a new possibility to probe interiors of massive stars. There are only a
few massive (masses of components $\gtrsim 2 $M$_\odot$) systems of this type
known. Using TESS data from the first 16 sectors, we searched for new massive
heartbeat stars and TEOs using a sample of over 300 eccentric spectroscopic
binaries. We analysed TESS 2-min and 30-min cadence data. Then, we fitted
Kumar's analytical model to the light curves of stars showing heartbeats and
performed times-series analysis of the residuals searching for TEOs and
periodic intrinsic variability. We found 20 massive heartbeat systems, of which
seven show TEOs. The TEOs occur at harmonics of orbital frequencies in the
range between 3 and 36, with the median value equal to 9, lower than those in
known Kepler systems with TEOs. The most massive system in this sample is the
quadruple star HD 5980, a member of Small Magellanic Cloud. With the total mass
of $\sim$150 M$_{\odot}$ it is the most massive system showing a heartbeat. Six
stars in the sample of the new heartbeat stars are eclipsing. Comparison of the
parameters derived from fitting Kumar's model and from light-curve modelling
shows that Kumar's model does not provide reliable parameters. Finally,
intrinsic pulsations of $\beta$ Cep, SPB, $\delta$ Sct, and $\gamma$ Dor-type
were found in nine heartbeat systems. This opens an interesting possibility of
studies of pulsation-binarity interaction and the co-existence of forced and
self-excited oscillations.
