time-frequency shifted gaussian function

I am trying to implement a function that generates a cyclic time and frequency shifted version of a gaussian function.

When I plot the function, the function looks like the one on the left while I desire to have a plot as shown on the right. Can somebody suggest me how can I attain the desired plot?

Following is my matlab code: clc close all

L = 256; % Length of the signal

% Define Parameters
a = 12; %time hop
b = 16; %frequency hop  
M = L/b;

m = 0;  % frequncy index
n = 0;  % time index

sigma = 50;

fxn =zeros(L,1);

l=0:L-1;
for i=1:length(l)

fxn(i,1) = exp(-pi*((l(i)-n*a)^2)/(sigma^2)) * exp(1i*2*pi*m*(l(i)-n*a)/L);
end

fxn = (1/norm(fxn)) .* fxn;   %Normalization