We study the high-energy phase diagram of a two-dimensional spin-$frac{1}{2}$ Heisenberg model on a square lattice in the presence of disorder. The use of large-scale tensor network numerics allows us to compute the bi-partite entanglement entropy for systems of up to $30times7$ lattice sites. We demonstrate the existence of a finite many-body localized phase for large disorder strength $W$ for which the eigenstate thermalization hypothesis is violated. Moreover, we show explicitly that the area law holds for excited states in this phase and determine an estimate for the critical $W_{rm{c}}$ where the transition to the ergodic phase occurs.
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