In virtual reality (VR) applications, 360-degree images play a pivotal role in crafting immersive experiences and offering panoramic views, thus improving user Quality of Experience (QoE). However, the voluminous data generated by 360-degree images poses challenges in network storage and bandwidth. To address these challenges, we propose a novel Activation Map-based Vector Quantization (AM-VQ) framework, which is designed to reduce communication overhead for wireless transmission. The proposed AM-VQ scheme uses the Deep Neural Networks (DNNs) with vector quantization (VQ) to extract and compress semantic features. Particularly, the AM-VQ framework utilizes activation map to adaptively quantize semantic features, thus reducing data distortion caused by quantization operation. To further enhance the reconstruction quality of the 360-degree image, adversarial training with a Generative Adversarial Networks (GANs) discriminator is incorporated. Numerical results show that our proposed AM-VQ scheme achieves better performance than the existing Deep Learning (DL) based coding and the traditional coding schemes under the same transmission symbols.