The origin of the hardware/software theory comes from the fact that Neo sees the Matrix in green code but he sees machines in the real world in gold code.
The Matrix and "software" programs:
The real world and "hardware" machines:
If Seraph's code obeys the color convention, this implies that he is a real machine jacked into the Matrix from the real world (somewhat similarly to the humans jacked into the Matrix -- they have real bodies but are also in the Matrix).1 In contrast, purely software programs like the Agents do not have bodies in the real world.
Ultimately, we don't know enough about Seraph's origins to explain why his code is gold vs. green. Since Seraph is believed to be a Seraphim (a program that performed the function of the Agents in the original Paradise Matrix), we would expect to see his code in green as we see the Agents'. He may have gold code because the Seraphim may have been real machines jacked into the Matrix (and the use of purely software Agents was developed later), or it may have something to do with his special role of guarding the Oracle ("that which matters most").
1 Humans appear in green code in the Matrix, too. My point here is not that "having a real body = having gold code", it's an analogy to having a real body vs. being a purely software program with no body in the real world. The code appearance of humans does not have the same convention as the machines' -- humans appear in green in the Matrix, but don't have any code color in the real world (see, e.g., Neo in the above image).