In Gimp there is a plugin named grid which is very simple to use.
Plugin parameters are width (of the lines), spacing (between lines) and offset from the top left corner.
You need to calculate the value of the spacing (or the dimension of the image), but it is very simple. For example, assuming that you want a 40x40 px peg with a border width of 2 px, you need a 632x632 px image, where 632=(40+2)*15+2.
Starting from a white image, the grid plugin is in
Filters->Render->Pattern->Grid and you can set your values (width=2, spacing=42, offset=1)
Obtained the grid you can fill the pegs:
Now, you need to add the text and center it on the pegs. Here can be useful the Align tool.
Write your text (it is in his own layer) and then select (with the magic wand tool) the peg in which the text should be centered:
Align tool and choose in his options to be relative to selection. The pointer is now a hand, select the text:
And use the tool to center it on the selection:
Repeat until done...
So, it's possible, but surely it's simpler in Inkscape or in Illustrator (or, perhaps, you can write the grid as an html page or use Excel or similar and take a screenshot). A ready made SVG grid is here, on Wikimedia Commons.