This is the first 11-square I have found by entirely automatic means. It took as long as finding a thousand 10-squares. In finding this square, 200,000 million squares complete in the first four rows had to be discarded, including 84000 squares complete to midway or later in the last row.
"The Eleven Square - Take Two,"
Word Ways: Vol. 38
, Article 3.
Available at: https://digitalcommons.butler.edu/wordways/vol38/iss2/3