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 Kumars 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 Kumars model and from light-curve modelling shows that Kumars 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.
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