Jelly, 1321 + 3716 = 5037 bytes
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Just compression of current bests on esolangs. There is probably a way to evaluate a subset of BF programs such that they will terminate and yield the shortest solutions that'd beat this naive program. There may well also be a way to beat this by a smarter pattern-based or factorisation-building program.
“ ... ’ṃ“+[><-]¶ - Link: no arguments “ ... ’ - a really big number compressed as base 250 “+[><-]¶ - list of characters ['+','[','>','<','-',']','\n'] ṃ - base decompress i.e. use those as the base 7 digits [1,2,3,4,5,6,0]