  Homological product codes are a class of codes that can have improved
distance while retaining relatively low stabilizer weight. We show how to build
union-find decoders for these codes, using a union-find decoder for one of the
codes in the product and a brute force decoder for the other code. We apply
this construction to the specific case of the product of a surface code with a
small code such as a $[[4,2,2]]$ code, which we call an augmented surface code.
The distance of the augmented surface code is the product of the distance of
the surface code with that of the small code, and the union-find decoder, with
slight modifications, can decode errors up to half the distance. We present
numerical simulations, showing that while the threshold of these augmented
codes is lower than that of the surface code, the low noise performance is
improved.
