$ docker push nosuchimage
The push refers to repository [docker.io/library/nosuchimage]
An image does not exist locally with the tag: nosuchimage

echo $?
1

$ docker push busybox
The push refers to repository [docker.io/library/busybox]
195be5f8be1d: Layer already exists
[DEPRECATION NOTICE] registry v2 schema1 support will be removed in an upcoming release. Please contact admins of the docker.io registry NOW to avoid future disruption. More information at https://docs.docker.com/registry/spec/deprecated-schema-v1/
errors:
denied: requested access to the resource is denied
unauthorized: authentication required

echo $?
1

$ docker push --quiet nosuchimage
docker.io/library/nosuchimage

$ echo $?
0

$ docker push --quiet busybox
docker.io/library/busybox

$ echo $?
0