By interfacing computing logic directly to the DRAM banks, bank-level Compute-near-Memory (CnM) architectures promise to mitigate the bottleneck at the memory interconnect. While this computation paradigm heavily reduces the energy requirements for data movement across the system, current solutions fail to co-optimize hardware and software to further increase efficiency. Instead, in this manuscript we present SideDRAM, a co-designed bank-level CnM architecture to enable massively parallel and energy-efficient computations near DRAM. In contrast with past solutions, we support flexible data typing and heterogeneous quantization, relying on the robustness of workloads to employ small bitwidths, and enable a row-wide access to the banks to exploit parallelism and spatial locality. As a result, SideDRAM integrates (1) software-defined SIMD (SoftSIMD) datapaths, supporting low-energy computing with flexible precision, (2) an interface to the banks based on very wide registers (VWRs), enabling asymmetric data access to both utilize the full DRAM bank bandwidth and leverage data locality at the datapath, and (3) a low-overhead distributed control plane, allowing the efficient handling of variable data typing. We benchmark SideDRAM as a near-DRAM solution by analyzing the area, performance and energy consumption of an HBM2 CnM channel executing heterogeneously quantized machine learning models. The results show that, compared to the state-of-the-art FIMDRAM design, energy improvements of up to 67% are achieved when a DeiT-S inference is executed with a batch size of 16 under the same area constraints, resulting in energy-delay-area product (EDAP) savings that reach 83%. When comparing to a massively parallel mixed-signal CnM solution, SideDRAM consistently obtains similar performance and better energy efficiency results (geomean of 15x improvement across workloads) at a lower area overhead.