Electromagnetic waves possessing orbital angular momentum (OAM) are powerful tools for applications in optical communications, quantum technologies, and optical tweezers. Recently, they have attracted growing interest since they can be harnessed to detect peculiar helical dichroic effects in chiral molecular media and in magnetic nanostructures. In this work, we perform single-shot per position ptychography on a nanostructured object at a seeded free-electron laser, using extreme ultraviolet OAM beams of different topological charge orders ℓ generated with spiral zone plates. By controlling ℓ, we demonstrate how the structural features of OAM beam profiles determine an improvement of about 30% in image resolution with respect to conventional Gaussian beam illumination. This result extends the capabilities of coherent diffraction imaging techniques, and paves the way for achieving time-resolved high-resolution (below 100 nm) microscopy on large area samples.