  We use the $1/N_c$ expansion of QCD to analyze the spectrum of positive
parity resonances with strangeness $S = 0, -1, -2$ and -3 in the 2--3 GeV mass
region, supposed to belong to the $[\textbf{56},4^+]$ multiplet. The mass
operator is similar to that of $[\textbf{56},2^+]$, previously studied in the
literature. The analysis of the latter is revisited. In the $[\textbf{56},4^+]$
multiplet we find that the spin-spin term brings the dominant contribution and
that the spin-orbit term is entirely negligible in the hyperfine interaction,
in agreement with constituent quark model results. More data are strongly
desirable, especially in the strange sector in order to fully exploit the power
of this approach.}
