Recently Bachoc and Gaborit introduced the notion of s-extremality for binary self-dual codes, generalizing Elkies' study on the highest possible minimum weight of the shadows of binary self-dual codes. In this paper, we introduce a concept of s-extremality for additive self-dual codes over F 4 , give a bound on the length of these codes with even distance d, classify them up to minimum distance d = 4, give possible lengths (only strongly conjectured for odd d) for which there exist s-extremal codes with 5 les d les 11, and give five s-extremal codes with d = 7 as well as four new s-extremal codes with d = 5. We also describe codes related to s-extremal codes