diff --git a/src/sage/combinat/words/morphism.py b/src/sage/combinat/words/morphism.py
index fe77b50fcfd..fae124378a8 100644
--- a/src/sage/combinat/words/morphism.py
+++ b/src/sage/combinat/words/morphism.py
@@ -2092,6 +2092,15 @@ def language(self, n, u=None):
              ...
              word: 1010010001,
              word: 1010010100]
+
+        Test non-extendable D0L-language (Thue-Morse with cube axiom).
+        This ensures factors from the axiom and early iterations are included::
+
+            sage: m = WordMorphism('0->01,1->10')
+            sage: Word('000') in m.language(3, Word('000'))
+            True
+            sage: Word('010101') in m.language(6, Word('000'))
+            True
         """
         W = self.domain()
         if self.codomain() != W:
@@ -2123,10 +2132,19 @@ def language(self, n, u=None):
         # of two letter words
         L2 = (w for w in self._language_naive(3, u) if len(w) == 2)
         L = set()
-        for u in L2:
-            v = im[u[0]] + im[u[1]]
+        for v in L2:
+            w = im[v[0]] + im[v[1]]
+            for k in range(len(w) - n + 1):
+                L.add(w[k:k + n])
+
+        # Also add factors from the axiom and early iterations
+        # to handle non-extendable elements in the D0L-language
+        v = u
+        for _ in range(p + 1):
             for k in range(len(v) - n + 1):
                 L.add(v[k:k + n])
+            v = self(v)
+
         return L
 
     def conjugate(self, pos):