Attractive magnetic phenomena such as skyrmions and all-optical-switching are found in ferrimagnetic materials and structures. Magneto-optical microscopy with extreme-UV and X-rays offers a unique element-specific probe of the magnetization state, however, it is presently limited to synchrotrons and free-electron lasers. This work is the first demonstration of nanoscale magnetic imaging with high-harmonic generation (HHG) from lasers. We quantitatively map the phase- and absorption XMCD (X-ray magnetic circular dichroism) contrast using circularly polarized HHG, at a resolution below 50 nm. This result opens the path towards element-specific probing of magnetic dynamics at the nanometer- and femtosecond-scales, even at a ferrimagnetic compensation point.