  We describe a computationally-efficient heuristic algorithm based on a
renormalization-group procedure which aims at solving the problem of finding
minimal surface given its boundary (curve) in any hypercubic lattice of
dimension $D>2$. We use this algorithm to correct errors occurring in a
four-dimensional variant of the toric code, having open as opposed to periodic
boundaries. For a phenomenological error model which includes measurement
errors we use a five-dimensional version of our algorithm, achieving a
threshold of $4.35\pm0.1\%$. For this error model, this is the highest known
threshold of any topological code. Without measurement errors, a
four-dimensional version of our algorithm can be used and we find a threshold
of $7.3\pm0.1\%$. For the gate-based depolarizing error model we find a
threshold of $0.31\pm0.01\%$ which is below the threshold found for the
two-dimensional toric code.
