Add automatic publish of docker images

.changeset/three-tables-mix.md

@@ -0,0 +1,5 @@
+---
+"bits-to-dead-trees": patch
+---
+
+Add automatic publish of docker images

.github/workflows/build-docker-image.yml

@@ -0,0 +1,30 @@
+name: Build and Push Docker Image
+
+on:
+  push:
+    tags:
+      - "v*"
+
+concurrency: ${{ github.workflow }}-${{ github.ref }}
+
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout Repo
+        uses: actions/checkout@v3
+
+      - name: Login to GitHub Container Registry
+        uses: docker/login-action@v1
+        with:
+          registry: ghcr.io
+          username: ${{ github.repository_owner }}
+          password: ${{ secrets.GITHUB_TOKEN }}
+
+      - name: Build and push builder image
+        uses: docker/build-push-action@v2
+        with:
+          file: Dockerfile
+          push: true
+          tags: |
+            ghcr.io/${{ github.repository }}:${{ github.ref_name }}