A code is a quaternary linear code if is a subgroup of ℤ4. In this paper, the rank and dimension of the kernel for ℤ4- linear codes, which are the corresponding binary codes of quaternary linear codes, are studied. The possible values of these two parameters for ℤ4-linear codes, giving lower and upper bounds, are established. For each possible rank r between these bounds, the construction of a ℤ4-linear code with rank r is given. Equivalently, for each possible dimension of the kernel k, the construction of a ℤ4- linear code with dimension of the kernel k is given.