cfn_tpl_excerpt.yml

x-amazon-apigateway-integration:
  #...
  responses:
    ".*\\\"code\\\":\\\"[A-Z_]+_NOT_FOUND\\\".*":
      statusCode: "404"
      responseParameters:
        method.response.header.Content-Type : "'application/json'"
      responseTemplates:
        application/json: |
          #set ($errorMessageObj = $util.parseJson($input.path('$.errorMessage')))
          {
            "code" : "$errorMessageObj.code",
            "message" : "$errorMessageObj.public_message"
          }