[CI/CD] Wiki push changes no permission with Deploy Key

Summary

Hi, the idea it's push docs change in a project to a general project documentation. I use a CI/CD that push to the documetnacion wiki the asccidoc changes. But when the CI/CD do the step the return is:

GitLab: You are not allowed to write to this project's wiki. fatal: Could not read from remote repository.

Steps to reproduce

I create a SSH key and config the public key to the documentation.wiki and the private key to the porject that wants to publish to the documentation wiki. I create a gitlab-ci.yml with then step:

update-doc:
  stage: update-doc
  image: ruby:2.1
  script:
    # Run ssh-agent (inside the build environment)
     # - apk add --no-cache bash git openssh-client
     - eval $(ssh-agent -s)
     # add ssh key stored in SSH_PRIVATE_KEY variable to the agent store
     - ssh-add <(echo "$ssh_doc_key")
     - mkdir -p ~/.ssh
     - echo -e "Host *\n\tStrictHostKeyChecking no\n\n" > ~/.ssh/config
     - ssh git@gitlab.com
     - git config --global user.name $GITLAB_USER_NAME
     - git config --global user.email $GITLAB_USER_EMAIL
     - git clone git@gitlab.com:<group_repo>/documentation.git
     - cd documentation
     - cp $CI_PROJECT_DIR/src/main/asciidoc/*.adoc .
     - git add .
     - git commit -m "update wiki cobos"
     - git push --force

What is the current bug behavior?

GitLab: You are not allowed to write to this project's wiki. fatal: Could not read from remote repository.

What is the expected correct behavior?

I supossed that wiki permissions have the same access level as the users of the group or the deploy keys added

(What you should see instead)

Greetings.