The well-known quasar SDSS J095253.83+011421.9 (J0952+0114) at z=3.02 has one of the most peculiar spectra discovered so far, showing the presence of narrow Ly$\alpha$ and broad metal emission lines. Although recent studies have suggested that a Proximate Damped Ly$\alpha$ system (PDLA) causes this peculiar spectrum, the origin of the gas associated with the PDLA is unknown. Here we report the results of MUSE observations that reveal a new giant ($\approx$ 100 physical kpc) Lyman $\alpha$ nebula. The detailed analysis of the Ly$\alpha$ velocity, velocity dispersion, and surface brightness profiles suggests that the J0952+0114 Ly$\alpha$ nebula shares similar properties of other QSO nebulae previously detected with MUSE, implying that the PDLA in J0952+0144 is covering only a small fraction of the QSO emission solid angle. We also detected bright and spectrally narrow CIV$\lambda$1550 and HeII$\lambda$1640 extended emission around J0952+0114 with velocity centroids similar to the peak of the extended and central narrow Ly$\alpha$ emission. The presence of a peculiarly bright, unresolved, and relatively broad HeII$\lambda$1640 emission in the central region at exactly the same PDLA redshift hints at the possibility that the PDLA originates in a clumpy outflow with a bulk velocity of about 500 km/s. The smaller velocity dispersion of the large scale Ly$\alpha$ emission suggests that the high-speed outflow is confined to the central region. Lastly, the derived spatially resolved HeII/Ly$\alpha$ and CIV/Ly$\alpha$ maps show a positive gradient with the distance to the QSO hinting at a non-homogeneous ionization parameter distribution.