After the optimal parameters of additive quaternary codes of dimension k<=3 have been determined in 1, there was some activity to settle the next case of dimension k=3.5 2,3. Here we complete dimensions k=3.5 and k=4. We also solve the problem of the optimal parameters of additive quaternary codes of arbitrary dimension when assuming a sufficiently large minimum distance.
Sascha Kurz (Thu,) studied this question.