Near-field enhancement of the electric field by metallic nanostructures is important in non-linear optical applications such as surface enhanced Raman scattering. One approach to producing strong localization of the electric field is to couple a dark, non-radiating plasmonic mode with a broad dipolar resonator that is detectable in the far-field. However, characterizing or predicting the degree of the coupling between these modes for a complicated nanostructure can be quite challenging. Here we develop a robust method to solve the T-matrix, the matrix that predicts the scattered electric fields of the incident light, based on finite-difference time-domain (FDTD) simulations and least square fitting algorithms. This method allows us to simultaneously calculate the T-matrix for a broad spectral range. Using this method, the coupling between the electric dipole and quadrupole modes of spiky nanoshells is evaluated. It is shown that the built-in disorder in the structure of these nanoshells allows for coupling between the dipole modes of various orientations as well as coupling between the dipole and the quadrupole modes. A coupling strength of about 5% between these modes can explain the apparent interference features observed in the single particle scattering spectrum. This effect is experimentally verified by single particle backscattering measurements of spiky nanoshells. The modal interference in disordered spiky nanoshells can explain the origin of the spectrally broad quadrupole resonances that result in strong Quadrupole Enhanced Raman Scattering (QERS) in these nanoparticles.