Since you have no y-axis, here's how I would do this: Create an Excel spreadsheet with the numbers 1-35 in Column A, and with the numbers -2 to 19 along the top of Row 1.
In each intersection of the right number with the right color value, enter a 0.
Graph this range, using a line chart with point markers. You will end up with various points along the x-axis, with different colors and shapes, according to the distribution in your table. Now you should completely remove the y-axis (no line, no fill, no labels, no ticks), gridlines, and legend.
Finally, I would edit the various data series, by removing the lines (leaving the markers), and setting all the line markers to use the same shape, with only the colors differing.