Context. Linking atmospheric characteristics of planets to their formation pathways is a central theme in the study of extrasolar planets. Although the 12C/13C isotope ratio shows little variation in the Solar System, the atmosphere of a super-Jupiter was recently shown to be rich in 13CO, possibly as a result of dominant ice accretion beyond the CO snow line during its formation. Carbon isotope ratios are therefore suggested to be a potential tracer of formation pathways of planets. Aims. In this work, we aim to measure the 12CO/13CO isotopologue ratio of a young, isolated brown dwarf. While the general atmospheric characteristics of young, low-mass brown dwarfs are expected to be very similar to those of super-Jupiters, their formation pathways may be different, leading to distinct isotopologue ratios. In addition, such objects allow high-dispersion spectroscopy at high signal-to-noise ratios. Methods. We analysed archival K-band spectra of the L dwarf 2MASS J03552337+1133437 taken with NIRSPEC at the Keck telescope. A free retrieval analysis was applied to the data using the radiative transfer code petitRADTRANS coupled with the nested sampling tool PyMultiNest to determine the isotopologue ratio 12CO/13CO in its atmosphere. Results. The isotopologue 13CO is detected in the atmosphere through the cross-correlation method at a signal-to-noise of ~8.4. The detection significance is determined to be ~9.5σ using a Bayesian model comparison between two retrieval models (including or excluding 13CO). We retrieve an isotopologue 12CO/13CO ratio of 97−18+25 (90% uncertainty), marginally higher than the local interstellar standard. Its C/O ratio of ~0.56 is consistent with the solar value. Conclusions. Although only one super-Jupiter and one brown dwarf now have a measured 12CO/13CO ratio, it is intriguing that they are different, possibly hinting to distinct formation pathways. Regardless of spectroscopic similarities, isolated brown dwarfs may experience a top-down formation via gravitational collapse, which resembles star formation, while giant exoplanets favourably form through core accretion, which potentially alters isotopologue ratios in their atmospheres depending on the material they accrete from protoplanetary disks. This further emphasises atmospheric carbon isotopologue ratio as a tracer of the formation history of exoplanets. In the future, analyses such as those presented here should be conducted on a wide range of exoplanets using medium-to-high-resolution spectroscopy to further assess planet formation processes.