We describe a new approach to improve the success rate of symbol decoding with very high-order modulations at receivers equipped with low-resolution analog-to-digital converters (ADC). The proposed method is based on generating self-inflicting pseudo-random white noise signal at the receiving antenna array in order to improve the performance of spatial oversampling. As the optimal amount of this artificially induced noise strongly depends on the ADC resolution, transmit symbol modulation, and the number of receive antennas, we design an adaptation mechanism to render an acceptable balance for successful decoding between the inner- and outer-region symbols of the constellation. Numerical findings demonstrate, for the first time, that the feasibility of high-order symbol modulations (e.g., 64/256-QAM) is within reach by low-resolution ADCs.