As a point of interest to monks trying to solve this, the dimensions of a character in the <code> font on my screen are: 7 pixels wide, 12 pixels from baseline to baseline (that's counting from the first pixel below the baseline to the first pixel above the baseline of the next line). So a square on screen is 12x7 in characters. I got these numbers by zooming in on a screen shot. YMMV.

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If I were trying to write this, I'd probably go a brute force route first. Count the characters, estimate the size of a circle that would encompass them, and then start with a circle somewhat larger than that. I'd loop over circles of progressively smaller sizes. At each size, I'd try to break the lines to (handwave ahead) fit the edges of the circle and measure how close I get. Whatever formatting gets closest wins. I'd be tempted to insert an extra space between some words to get the edges to come out right (as with fully justified text).