Directly imaging exoplanets is challenging because quasi-static phase aberrations in the pupil plane (speckles) can mimic the signal of a companion at small angular separations. Kernel phase, which is a generalization of closure phase (known from sparse aperture masking), is independent of pupil plane phase noise to second order and allows for a robust calibration of full pupil, extreme adaptive optics observations. We applied kernel phase combined with a principal component based calibration process to a suitable but not optimal, high cadence, pupil stabilized L' band (\(3.8~\mu\text{m}\)) data set from the ESO archive. We detect eight low-mass companions, five of which were previously unknown, and two have angular separations of \(\sim0.8\)-\(1.2~\lambda/D\) (i.e. \(\sim80\)-\(110~\text{mas}\)), demonstrating that kernel phase achieves a resolution below the classical diffraction limit of a telescope. While we reach a \(5\sigma\) contrast limit of \(\sim1/100\) at such angular separations, we demonstrate that an optimized observing strategy with more diversity of PSF references (e.g. star-hopping sequences) would have led to a better calibration and even better performance. As such, kernel phase is a promising technique for achieving the best possible resolution with future space-based telescopes (e.g. JWST), which are limited by the mirror size rather than atmospheric turbulence, and with a dedicated calibration process also for extreme adaptive optics facilities from the ground.