FDTD (Finite Difference Time Domain) is a mathematically intensive method of analysing electromagnetic structures. For me anyway, it is definitely hard sums!
Since you were able to write the code for FDTD equations derived directly from Maxwell's curl equations, then I guess you already know the features an antenna structure has to have to radiate.
First, we need to be clear about the near zero S11.
Since S11 is the input reflection coefficient, then it's worst value is 1 (all is reflected), and its most desired value is zero (no power reflected - all is radiated).
If instead, you meant S11 expressed in dB, then a value near 0dB is indeed a bad thing. A desired low reflection value would be fractional, giving negative values in dB eg. -25dB being the good thing.
One possible cause of analysis problems in FDTD is inadvertently using a forcing voltage source where the internal resistance is zero. This model generates non-physical reflections. The antenna feed point should be driven by a voltage signal in series with a resistance which can be varied to suit.
It is perfectly possible have a antenna shape that works well, yet it also has a very low radiation resistance. Additionally, the feed does not have to be at a place where the driving point impedance is resistive. It can be where the impedance is complex.
I choose an arbitrary example of a magnetic loop antenna which can have radiation resistance lower than 0.5 Ohms, and needs to be made of substantial diameter copper tube to make the physical resistance much less than that, to get efficiency.
Such an antenna, connected to a source, and analysed for S11 at 50 Ohms reference, would reflect nearly all. But when driven via a matching network, maybe with a coupling arrangement, it could then present a good S11.
Without knowing your antenna structure, we cannot tell if the (maybe) poor S11 is because of the structure shape, or because of the mathematical model. Beyond the speculations above, I regret I may not be able to help you much.