Observations in the lowest Murchison Widefield Array (MWA) band between 75 and 100 MHz have the potential to constrain the distribution of neutral hydrogen in the intergalactic medium at redshift ∼13–17. Using 15 h of MWA data, we analyse systematics in this band such as radio-frequency interference (RFI), ionospheric and wide field effects. By updating the position of point sources, we mitigate the direction-independent calibration error due to ionospheric offsets. Our calibration strategy is optimized for the lowest frequency bands by reducing the number of direction-dependent calibrators and taking into account radio sources within a wider field of view. We remove data polluted by systematics based on the RFI occupancy and ionospheric conditions, finally selecting 5.5 h of the cleanest data. Using these data, we obtain 2σ upper limits on the 21 cm power spectrum in the range of |$0.1~ h~{\mathrm{ Mpc}}^{-1}\lessapprox k \lessapprox 1 ~ ~h~{\mathrm{ Mpc}}^{-1}$| and at z = 14.2, 15.2, and 16.5, with the lowest limit being |$6.3\times 10^6 ~\rm mK^2$| at |$k=0.14 ~h~{\mathrm{ Mpc}}^{-1}$| and at z = 15.2 with a possibility of a few per cent of signal loss due to direction-independent calibration. [ABSTRACT FROM AUTHOR]