Korchmaros and Nagy [Hermitian codes from higher degree places. J Pure Appl Algebra, doi: 10. 1016/j.jpaa.2013.04.002, 2013] computed the Weierstrass gap sequence G(P) of the Hermitian function field F q 2 ( H ) at any place P of degree 3, and obtained an explicit formula of the Matthews-Michel lower bound on the minimum distance in the associated differential Hermitian code C Ω ( D,mP ) where the divisor D is, as usual, the sum of all but one 1-degree F q 2 -rational places of F q 2 ( H ) and m is a positive integer. For plenty of values of m depending on q , this provided improvements on the designed minimum distance of C Ω ( D,mP ). Further improvements from G(P) were obtained by Korchmaros and Nagy relying on algebraic geometry. Here slightly weaker improvements are obtained from G(P) with the usual function-field method depending on linear series, Riemann-Roch theorem and Weierstrass semigroups. We also survey the known results on this subject.