We present a study of a quantum controlled–controlled-not gate, implemented in a chain of three nuclear spins weakly Ising interacting between all of them, that is, taking into account first and second neighbour spin interactions. This implementation is done using a single resonant π-pulse on the initial state of the system (digital and superposition). The fidelity parameter is used to determine the behaviour of the CCN quantum gate as a function of the ratio of the second neighbour interaction coupling constant to the first neighbour interaction coupling constant (J′/J). We found that for J′/J ⩾ 0.02 we can have a well-defined CCN quantum gate.