An exploration of the $4mu$, di-charmonium channel in search for a full-charm tetraquark of the form $cc\bar{c}\bar{c}$ is conducted using the ATLAS detector with $140\text{ fb}^{-1}$ of $pp$ data at $\sqrt{s}=13\text{ TeV}$. Both the di-$J/\psi$ and the $J/\psi+\psi(2S)$ channels are explored and excesses over the background corresponding to a resonance at $6.9\text{ GeV}$ are seen with statistical significance of $>5\;\sigma$ and $4.7\;\sigma$, respectively. At lower mass ranges, a broader structure can be observed, though its nature cannot be discerned with current data.