It's not clear whether 38cm is the width/depth or the height. If it is 59cm deep and 38 high it's a good size - although only just tall enough for a syrian and syrian wheel. If it is only 38cm deep (wide) it could be a bit on the narrow side as those are maximum measurements not allowing for sloping sides. Some bins crack easily when you cut them which is something to consider.
The best bin I know size-wise is the largest RUB bin but it's not cheap (£39.95) - it is good quality apparently and easier to make into a bin cage than some others due to the quality of the plastic for cutting. It has a good depth and they are easily stackable apparently.
Really Useful 145 Litre Clear Stacking Storage Box with Locking Lids
The internal dimensions are good - 71cm x 54.5cm deep x 40cm tall. Externally it is 81cm x 62cm deep by 43cm tall.