Context. Accretion among planetary mass companions is a poorly understood phenomenon, due to the lack of both observational and theoretical studies. The detection of emission lines from accreting gas giants facilitates detailed investigations into this process. Aims. This work presents a detailed analysis of Balmer lines from one of the few known young, planetary-mass objects with observed emission, the isolated L2γ dwarf 2MASS J11151597+1937266 with a mass between 7 and 21 M_Jup and an age of 5–45 Myr, located at 45 ± 2 pc. Methods. We obtained the first high-resolution (R ~ 50 000) spectrum of the target with VLT/UVES, an echelle spectrograph operating in the near-ultraviolet to visible wavelengths (3200–6800 Å). Results. We report several resolved hydrogen (H I; H3–H6) and helium (He I; λ5875.6) emission lines in the spectrum. Based on the asymmetric line profiles of Hα and Hβ, the 10% width of Hα (199 ± 1 km s^‑1), tentative He I λ6678 emission, and indications of a disk from mid-infrared excess, we confirm ongoing accretion at this object. Using the Gaia update of the parallax, we revise its temperature to 1816 ± 63 K and radius to 1.5 ± 0.1 R_Jup. Analysis of observed H I profiles using a 1D planet-surface shock model implies a pre-shock gas velocity, v₀ = 120_‑40^{+ 80} km s^‑1, and a pre-shock density, log(n₀/cm^‑3) = 14_‑5^{+ 0}. The pre-shock velocity points to a mass, M_p = 6_‑4^{+ 8} M_Jup, for the target. Combining H I line luminosities (L_line) and planetary L_line‑L_acc (accretion luminosity) scaling relations, we derived a mass accretion rate, Ṁ_acc = 1.4_‑0.9^{+ 2.8} × 10^‑8 M_Jup yr^‑1. Conclusions. The line-emitting area predicted from the planet-surface shock model is very small (~0.03%), and points to a shock at the base of a magnetospherically induced funnel. The Hα profile exhibits a much stronger flux than predicted by the model that best fits the rest of the H I profiles, indicating that another mechanism than shock emission contributes to the Hα emission. Comparison of line fluxes and Ṁ_acc from archival moderate-resolution SDSS spectra indicate variable accretion at 2MASS J11151597+1937266.