The Euroball-IV γ-detector array, equipped with the ancillary charged particle detector array DIAMANT was used to study the residues of the fusion reaction 64Ni ⇒ 128Ba at Ebeam = 255 and 261 MeV, in an attempt to reach the highest anguar momentum and verify the existence of predicted hyperdeformed rotational bands. No discrete hyperdeformed bands were identified, but nevertheless a breakthrough was obtained a systematic search for rotational ridge structure with very large moments of inertia J (2) ≥ 100 ℏ2 MeV(-1), in agreement with theoretical predictions for hyperdeformed shapes. Evidence for hyperdeformiation was obtained by charged particle + γ-ray gating, selectiong triple correlated ridge structures in the continuum of each of the nuclei, 118Te, 124Xe and 124,125Cs. In 7 additional nuclei, rotational ridges were also identified with J(2) = 71-77ℏ2Mev(-1), which most probably correspond to surperdeformed 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.