Your 225 Amp breaker is OK (48 VDC Rated?).
Using a basic NEC table:
And you need somewhere around 1 to 2/0 cable based on 150 Amp fuse/current draw.
If you are really going to use a 225 Amp breaker, 4/0 is the minimum suggested wire size. You can go smaller (NEC is pretty conservative)--But it is not bad to follow NEC for a safe and reliable system.
If you where going to go with 4 AWG cable, 140 amp draw, with a 1.0 voltage drop:
15 feet total (one way run) from battery bank to AC inverter of 4 AWG wiring
Voltage drop: 1.04Voltage drop percentage: 4.35%Voltage at the end: 22.96
Your battery bank of 4x 6 volt @ 428 AH (20 hour rate) * 2 parallel strings = 24 volts @ 856 AH battery bank.
That is a pretty "hefty" size bank... At around 800 AH, I like to suggest looking at the next higher voltage (48 volt battery bank in your case).
Your bank at 10% rate of charge would be 85.6 amps nominal recommended for good battery life. Your solar array (5% minimum, 10% nominal, 13% typical solar cost effective maximum) sized for this bank, would be around:
Note that the Outback is limited to 80 amps charging... And your battery at 10% rate of charge is ~86 amp charging. Your are at the limit for a single controller. if you want more solar, 2x controllers would be needed. Or, you change to a 48 volt battery bank (P=V*I -- double bank voltage, double maximum solar array wattage).
I did not find any "hours of sun" listings for Baja California--But if we assume 5 hours minimum as a good number for a dry southern climate. A 10% solar panel off grid system would supply (and here is a link that you may find a city near with similar weather):
.....In real world use in most climates, it's pretty rare to get little to no pv charge for two days.......
Just doing some searching for separate battery chargers to handle a 48v bank - doesn't look like there are many options out there, mostly finding charger/inverter combos in the 4000w neighborhood... maybe stick with a 24v bank?