Dual-function radar-communications (DRFC) strategies aim to embed communication symbols into the radar waveforms, which serve to alleviate the spectrum congestion problem. In this context, frequency-hopping code selection (FHCS) has been proposed as an effective DFRC approach in frequency-hopped multiple-input multiple-output (MIMO) radar. FHCS encodes the communication symbols through the selection from the available hops of the subset of hops to be assigned to the waveforms in each chip. In this manner, FHCS applies information embedding in the fast-time, thereby greatly increasing the achievable bit rate at the expense of increased impact on the radar performance. In this work, we propose an enhanced version of the FHCS scheme that ameliorates the resulting ambiguity function, thus improving the radar performance. Furthermore, we present a practical implementation scheme that employs a greedy divide-and-conquer approach. The performance of the proposed strategy is evaluated using simulations and the benefits to the radar ambiguity function are demonstrated.