Run Docker with same user as on local host and own mounted folders

I have a local folder (code) on my system, which belongs to my user.The local folder path is something like this:

- home-- my_user---- work------ projects-------- code

I want to run a Docker container and mount this folder in the container. I want this mounted folder to belong to the user I have on the local host, so I can access files, create them inside the container, and still own them on the local host.
Docker is running in rootless mode.

I'm using this Dockerfile:

FROM ubuntuARG UIDARG GIDARG USERNAME# Install necessary packages including python3-virtualenv and pipRUN apt-get update && apt-get install -y \    sudo \    wget \    python3 \    python3-pip \    python3-virtualenv \    python3-dev \    build-essential \    gitRUN ln -sf /usr/bin/python3 /usr/bin/python && \    ln -sf /usr/bin/pip3 /usr/bin/pip# Create a group with the specified GIDRUN groupadd -g ${GID} ${USERNAME}# Create a user with the specified UID and GID (-d creates home folder, -s selects shell)RUN useradd -d /home/${USERNAME} -u ${UID} -g ${GID} -s /bin/bash ${USERNAME}# Add the user to the sudoers fileRUN echo "${USERNAME} ALL=(ALL) NOPASSWD:ALL" >> /etc/sudoersRUN mkdir /home/${USERNAME}/code && chown ${USERNAME} /home/${USERNAME}/codeRUN echo "${USERNAME}"USER ${USERNAME}

I'm building the image with:

docker build --build-arg UID=$(id -u) --build-arg GID=$(id -g) --build-arg USERNAME=$(whoami) -t image_name -f Dockerfile .

And running it with:

docker run -it -v /home/my_user/work/projects/code/:/home/my_user/code image_name

Inside the container, my username, id and gid are the same as on the local host.
However, if I check the permissions, I see that the code folder still belongs to root:

total 8drwxrwxr-x 10 root root 4096 Jul 11 14:41 code

I tried running chown again from the container:

chown -R my_user code/

but I get:

chown: changing ownership of 'code/xxx': Operation not permitted

for all the files in the code folder.