Unique Random Id using all 62 characters

I am looking for a way to generate unique random ids that will be as short as possible (similar to url shorteners) either through code or using MSSQL (preferable).

I know this can be done using NEWID or CRYPT_GEN_RANDOM(), but these methods only use A-F and 0-9, while I am looking for a solution that will use all 62 characters (A-Z,a-z,0-9) and therefore obtain a much shorter id.