I assume your image is grayscale, right?
If I understand you correctly:
min_val=min(example_img(:));
max_val=max(example_img(:));
figure(1);
imshow(example_img, [min_val, max_val]);
% setting the color map of the image to whatever we want
% I chose parula here but you can use whatever colormap
set(gca, 'colormap', parula);
% this generates a single column colorbar the same height as your image
% mapping colors to your image values between the calculated minimum and maximum
% because you wanted it as an image i translated it back to uint8
colorColumn = uint8(linspace(double(min_val), double(max_val), size(example_img, 1))');
% this will stretch the color-bar to the same width as your image
colorBarIm = repmat(colorColumn, 1, size(example_img, 2));
% this will display the color bar image on a second figure
figure(2);
imshow(colorBarIm);
% flip the axis view point because images are shown from top to bottom
% but colorbars are displayed bottom-up
view(180, 90);
% setting the color map of the colorbar image to match the one
% we set for the actual image
set(gca, 'colormap', parula);
% You probably also want to show the values corresponding to the colormap
axis on;
% remove the x tick marks because they are usually meaningless ona colorbar
xticks([]);
