Context. The combination of high-contrast imaging with spectroscopy and polarimetry offers a pathway to studying the grain distribution and properties of debris disks in exquisite detail. Here, we focus on the case of a gas-rich debris disk around HD 141569A, which features a multiple-ring morphology first identified with SPHERE in the near-infrared.Aims. We obtained polarimetric differential imaging with SPHERE in the H-band to compare the scattering properties of the innermost ring at 44 au with former observations in total intensity with the same instrument. In polarimetric imaging, we observed that the intensity of the ring peaks in the south-east, mostly in the forward direction, whereas in total intensity imaging, the ring is detected only at the south. This noticeable characteristic suggests a non-uniform dust density in the ring. With these two sets of images, we aim to study the distribution of the dust to solve for the actual dust distribution.Methods. We implemented a density function varying azimuthally along the ring and generated synthetic images both in polarimetry and in total intensity, which are then compared to the actual data. The search for the best-fit model was performed both with a grid-based and an MCMC approach. Using the outcome of this modelization, we further measured the polarized scattering phase function for the observed scattering angle between 33° and 147° as well as the spectral reflectance of the southern part of the ring between 0.98 and 2.1 μm. We tentatively derived the grain properties by comparing these quantities with MCFOST models and assuming Mie scattering.Results. We find that the dust density peaks in the south-west at an azimuthal angle of 220°~238° with a rather broad width of 61°~127°. The difference in the intensity distributions observed in polarimetry and total intensity is the result of this particular morphology. Although there are still uncertainties that remain in the determination of the anisotropic scattering factor, the implementation of an azimuthal density variation to fit the data proved to be robust. Upon elaborating on the origin of this dust density distribution, we conclude that it could be the result of a massive collision when we account for the effect of the high gas mass that is present in the system on the dynamics of grains. In terms of grain composition, our preliminary interpretation indicates a mixture of porous sub-micron sized astro-silicate and carbonaceous grains.Conclusions. The SPHERE observations have allowed, for the first time, for meaningful constraints to be placed on the dust distribution beyond the standard picture of a uniform ring-like debris disk. However, future studies with a multiwavelength approach and additional detailed modeling would be required to better characterize the grain properties in the HD 141569 system.Read less <