A large and thriving family served as a clear sign of a leader's prosperity and standing. Having dozens of sons and grandsons traveling together on young donkeys [מצודת ציון] was a striking display of success, wealth, and high social rank during the judge's lifetime.
Riding these animals was a distinct symbol of importance and elevated status [מצודת דוד, רד״ק]. Because the family possessed such immense wealth and greatness, the sons and grandsons were completely freed from the daily burdens of manual labor and farming. They could easily afford the luxury of riding wherever they needed to go [רד״ק].
Furthermore, the presence of grandsons highlights the judge's remarkable longevity and personal triumph. He lived long enough to see his thirty grandsons reach maturity, growing old enough to ride the animals completely on their own [רד״ק, ביאור שטיינזלץ].