The following are a subset of the run-maximal strings for rho_2(67)

aababaababbabaababaababbababbabaababbababbaababbababbabaababbababba
aababbabaababbabaababaababbabaababaababaababbabaababaababbabaababaa
aababbabaababbababbabaababbababbabaababaababbababbabaababbababbabaa
aababbababbabaababbababbabaababbabaabbababbabaababbababbabaababbaba