There remains a need for the multiplexed detection of biomolecules at extremely low concentrations in fields of medical diagnostics, food safety, and security. Surface plasmon resonance imaging is an established biosensing approach in which the measurement of the intensity of light across a sensor chip is correlated with the amount of target biomolecules captured by the respective areas on the chip. In this work, we present a new approach for this method allowing for enhanced bioanalytical performance via the introduction of nanostructured sensing chip and polarization contrast measurement, which enable the exploitation of both amplitude and phase properties of plasmonic resonances on the nanostructures. Here we will discuss a complex theoretical analysis of the sensor performance, whereby we investigate aspects related to both the optical performance as well as the transport of the analyte molecules to the functionalized surfaces. This analysis accounts for the geometrical parameters of the nanostructured sensing surface, the properties of functional coatings, and parameters related to the detection assay. Based on the results of the theoretical analysis, we fabricated sensing chips comprised of arrays of gold nanoparticles (by electron-beam lithography), which were modified by a biofunctional coating to allow for the selective capturing of the target biomolecules in the regions with high sensitivity. In addition, we developed a compact optical reader with an integrated microfluidic cell, allowing for the measurement from 50 independent sensing channels. The performance of this biosensor is demonstrated through the sensitive detection of short oligonucleotides down to the low picomolar level.