Gaussian modulated sinusoidal wave

Hello there everyone! Recently I have started practicing FDTD codes (mainly one dimensional) and while implementing the gaussian modulated sinusoidal, I am facing problem. I am multiplying the two signals together within the loop of time-step, but getting weird figures. Also, I noticed my figures are plotted against the grid size, not against the time-step or time. I wonder if anyone knows a clear way how to implement it with a loop against time-step or time with an example? And also point what crucial points I am missing out here?Thanks in advance!