As a quick remark, there is a Brian2 implementation of this specific paper by Xu Zhang : https://github.com/zxzhijia/Brian2STDPMNIST The code is a couple of years old, though, and it does not get updated anymore (e.g. it is not compatible with Python 3 as it is). A number of people forked and adapted this example, though (e.g. https://github.com/sdpenguin/Brian2STDPMNIST), these later versions might have fixed some of the issues.
Quite a few people seem to be interested in this example, it would be great if some of you could get together and turn this into a working example that can be shared with the community. This is somewhat similar to Pattern recognition in Spiking Neural Nets using Brian2 in scope, so maybe @touches and @Ziaeemehr would be interested?