Found it, I was using the wrong transport type:
<bean id="mqQueue" class="com.ibm.mq.jms.MQQueue">
<property name="baseQueueName" value="..." />
<property name="targetClient">
<util:constant static-field="com.ibm.mq.jms.JMSC.MQJMS_CLIENT_NONJMS_MQ" />
</property>
</bean>
Instead it should have been:
<bean id="mqQueue" class="com.ibm.mq.jms.MQQueue">
<property name="baseQueueName" value="..." />
<property name="targetClient">
<util:constant static-field="com.ibm.mq.jms.JMSC.MQJMS_CLIENT_JMS_COMPLIANT" />
</property>
</bean>