  The excited states of $N=44$ $^{74}$Zn were investigated via $\gamma$-ray
spectroscopy following $^{74}$Cu $\beta$ decay. By exploiting $\gamma$-$\gamma$
angular correlation analysis, the $2_2^+$, $3_1^+$, $0_2^+$ and $2_3^+$ states
in $^{74}$Zn were firmly established. The $\gamma$-ray branching and $E2/M1$
mixing ratios for transitions de-exciting the $2_2^+$, $3_1^+$ and $2_3^+$
states were measured, allowing for the extraction of relative $B(E2)$ values.
In particular, the $2_3^+ \to 0_2^+$ and $2_3^+ \to 4_1^+$ transitions were
observed for the first time. The results show excellent agreement with new
microscopic large-scale shell-model calculations, and are discussed in terms of
underlying shapes, as well as the role of neutron excitations across the $N=40$
gap. Enhanced axial shape asymmetry (triaxiality) is suggested to characterize
$^{74}$Zn in its ground state. Furthermore, an excited $K=0$ band with a
significantly larger softness in its shape is identified. A shore of the $N=40$
``island of inversion'' appears to manifest above $Z=26$, previously thought as
its northern limit in the chart of the nuclides.
