Greatest perimeter polygon on a geoboard

This is a bit longer than Matt’s polygon.

[Improved based on Matt’s comment to this answer.]

{1, 10}, {1, 8}, {2, 8}, {4, 9}, {1, 7}, {3, 8}, {2, 7}, {5, 9}, {1,6}, {4, 8}, {3, 7}, {6, 9}, {2, 6}, {5, 8}, {1, 5}, {4, 7}, {3, 6},{7, 9}, {2, 5}, {6, 8}, {1, 4}, {5, 7}, {4, 6}, {8, 9}, {3, 5}, {7,8}, {2, 4}, {6, 7}, {1, 3}, {5, 6}, {4, 5}, {9, 9}, {3, 4}, {8, 8},{2, 3}, {7, 7}, {1, 2}, {6, 6}, {5, 5}, {9, 8}, {4, 4}, {8, 7}, {3,3}, {7, 6}, {2, 2}, {6, 5}, {1, 1}, {5, 4}, {4, 3}, {9, 7}, {3, 2},{8, 6}, {2, 1}, {7, 5}, {6, 4}, {9, 6}, {5, 3}, {8, 5}, {4, 2}, {7,4}, {3, 1}, {6, 3}, {9, 5}, {5, 2}, {8, 4}, {4, 1}, {7, 3}, {6, 2},{9, 4}, {5, 1}, {8, 3}, {7, 2}, {6, 1}, {8, 2}, {7, 1}, {8, 1}, {10,1}, {10, 8}, {9, 2}, {10, 9}, {9, 3}, {10, 10}, {3, 9}, {9, 10}, {2,9}, {8, 10}, {1, 10}

Length $32 \sqrt{2}+3 \sqrt{5}+15 \sqrt{13}+4 \sqrt{37}+16 \sqrt{41}+5 \sqrt{61}+125\approx 396.87859$.

The following plausibly-but-not-necessarily optimal modification of the above gives a perimeter of $383.61$, as

$126+22\sqrt{2}+5\sqrt{5}+16\sqrt{13}+16\sqrt{41}+5\sqrt{61}+2\sqrt{65}:$

$(1,10) - (1,9) - (1,8) - (3,9) - (2,8) - (4,9) - (1,7) - (3,8) - (2,7) - (5,9) - (1,6) - (4,8) - (3,7) - (6,9) - (2,6) - (5,8) - (1,5) - (4,7) - (3,6) - (7,9) - (2,5) - (6,8) - (1,4) - (5,7) - (4,6) - (8,9) - (3,5) - (7,8) - (2,4) - (6,7) - (1,3) - (5,6) - (4,5) - (9,9) - (3,4) - (8,8) - (2,3) - (7,7) - (1,2) - (6,6) - (5,5) - (9,8) - (4,4) - (8,7) - (3,3) - (7,6) - (2,2) - (6,5) - (1,1) - (5,4) - (4,3) - (9,7) - (3,2) - (8,6) - (2,1) - (7,5) - (6,4) - (9,6) - (5,3) - (8,5) - (4,2) - (7,4) - (3,1) - (6,3) - (9,5) - (5,2) - (8,4) - (4,1) - (7,3) - (6,2) - (9,4) - (5,1) - (8,3) - (7,2) - (9,3) - (6,1) - (8,2) - (7,1) - (8,1) - (10,1) - (10,9) - (9,2) - (10,10) - (2,9) - (9,10) - (1,10) $