The Euroball-IV \gamma -detector array, equipped with the ancillary charged particle detector array DIAMANT was used to study the residues of the fusion reaction $^{64}$Ni + $^{64}$Ni \Rightarrow $^{128}$Ba at E_{beam} = 255 and 261 MeV, in an attempt to reach the highest angular momentum and verify the existence of predicted hyperdeformed rotational bands. No discrete hyperdeformed bands were identified, but nevertheless a breakthrough was obtained through a systematic search for rotational ridge structures with very large moments of inertia J(2) \ge 100 {\mathchar h}^2 MeV^(-1), in agreement with theoretical predictions for hyperdeformed shapes. Evidence for hyperdeformation was obtained by charged particle + \gamma -ray gating, selecting triple correlated ridge structures in the continuum of each of the nuclei, $^ {118}$Te, $^{124}$Xe and $^{124,125}$Cs. In 7 additional nuclei, rotational ridges were also identified with J(2) = 71--77 {\mathchar h}^2 MeV^(-1), which most probably correspond to superdeformed shape. The angular distributions of the emitted charged particles show an excess in forward direction over expectations from pure compound evaporation, which may indicate that in-complete fusion plays an important role in the population of very elongated shapes.< Leer menos