Measuring the physical parameters of Coronal Mass Ejections (CMEs), particularly their entrained magnetic field, is crucial for understanding their physics and for assessing their geo-effectiveness. At the moment, only remote sensing techniques can probe these quantities in the corona, the region where CMEs form and acquire their defining characteristics. Radio observations offer the most direct means for estimating the magnetic field when gyrosynchontron emission is detected. In this work we measure various CME plasma parameters, including its magnetic field, by modelling the gyrosynchrotron emission from a CME. The dense spectral coverage over a wide frequency range provided by the Murchison Widefield Array (MWA) affords a much better spectral sampling than possible before. The MWA images also provide much higher imaging dynamic range, enabling us to image these weak emissions. Hence we are able to detect radio emission from a CME at larger distances ($4.73 R_odot$) than have been reported before. The flux densities reported here are amongst the lowest measured in similar works. Our ability to make extensive measurements on a slow and otherwise unremarkable CME suggest that with the availability of data from the new generation instruments like the MWA, it should now be possible to make routine direct detections of radio counterparts of CMEs.