Since the Toyota is making "Billions" for selling their oils which infact they are not actually manufacturing. They just buying from outside and tagging it as Toyota's oil. And people believe them like they believe that eating is necessary to live.
And now Suzuki also started the same strategy and we are again believing on them.
So firstly, lets believe that "Suzuki's own oil or their recommended oil" is absolutely not necessary to consider. Lets ignore them. Because this oil will be less suitable for Car but will help Suzuki to be rich enough.
Now, this Cultus euro II 2013 is the technology that Japan has already introduced probably couple of years back and also called Synthetic technology. But as the Cultus is manufactured in Pak. & as you said its with CNG Conversion, I would suggest followings
ZIC OW 5/20 or 5/30 Change it after driving every 5000 KM.
ZIC A+ ZIC A+ 5/20 or 5/30 Change it after driving 4500 KM.
Performa 5/40 Fully Synthetic (I love this oil personally).
Don't use/trust Havoline, Caltex, Castrol, Shell, Total, Zippex, Sinopec, Mobil, Toyota, etc. Mostly of them are locally packed oils and quality is not good.
Example: Toyota's Petron, Gazon, Excelron, etc. are designed to run more than 5000 KM (according to their broucher). But 99.99% people of Toyota itself will advise to change it after 3500~4000km as max. and do not over run upto 5000 KM. So we should be wise enough to understand that infact the quality of this oil is not good enough to run over 5K. They are just naming it. Say... they are calling "cakes" to the Pastries. Technically they are correct because Pastry is a piece of cake. But actually, its just a small part of cake and not full.
Congrats for your new car and wish you all the best.
At-least use half tank of "Hi Octane" at-least once in every 1500~2000 KM. Its good tip for Engine's long life.